system_prompt stringclasses 1
value | question stringlengths 60 5.92k | question_list listlengths 1 131 | gt_output stringlengths 1.03k 116k | thoughts_list listlengths 5 1.11k | system_list listlengths 10 10 | add_eos bool 1
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Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and iteration to develop w... | Return your final response within \boxed{}. The operation $\otimes$ is defined for all nonzero numbers by $a\otimes b =\frac{a^{2}}{b}$. Determine $[(1\otimes 2)\otimes 3]-[1\otimes (2\otimes 3)]$.
$\text{(A)}\ -\frac{2}{3}\qquad\text{(B)}\ -\frac{1}{4}\qquad\text{(C)}\ 0\qquad\text{(D)}\ \frac{1}{4}\qquad\text{(E)}\ \... | [
"Return your final response within \\boxed{}.",
"The operation $\\otimes$ is defined for all nonzero numbers by $a\\otimes b =\\frac{a^{2}}{b}$.",
"Determine $[(1\\otimes 2)\\otimes 3]-[1\\otimes (2\\otimes 3)]$.",
"$\\text{(A)}\\ -\\frac{2}{3}\\qquad$",
"$\\text{(B)}\\ -\\frac{1}{4}\\qquad$",
"$\\text{(C... | <|begin_of_thought|>
Okay, let me try to figure out this problem. So, we have this operation defined as a⊗b = a²/b. And we need to compute [(1⊗2)⊗3] - [1⊗(2⊗3)]. Then choose the correct answer from the options given. Alright, let's break it down step by step.
First, I need to remember that the operation ⊗ is not assoc... | [
"<|begin_of_thought|>\nOkay, let me try to figure out this problem. So, we have this operation defined as a⊗b = a²/b. And we need to compute [(1⊗2)⊗3] - [1⊗(2⊗3)]. Then choose the correct answer from the options given. Alright, let's break it down step by step.",
"First, I need to remember that the operation ⊗ is... | [
"Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions.",
"This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and iteration to... | true |
Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and iteration to develop w... | Return your final response within \boxed{}. Doug constructs a square window using $8$ equal-size panes of glass, as shown. The ratio of the height to width for each pane is $5 : 2$, and the borders around and between the panes are $2$ inches wide. In inches, what is the side length of the square window?
[asy] fill((0,0... | [
"Return your final response within \\boxed{}.",
"Doug constructs a square window using $8$ equal-size panes of glass, as shown.",
"The ratio of the height to width for each pane is $5 : 2$, and the borders around and between the panes are $2$ inches wide.",
"In inches, what is the side length of the square wi... | <|begin_of_thought|>
Okay, let me try to figure out this problem. So Doug has a square window made up of 8 equal-sized panes of glass. Each pane has a height to width ratio of 5:2. There are borders around and between the panes that are 2 inches wide. The question is asking for the side length of the square window in i... | [
"<|begin_of_thought|>\nOkay, let me try to figure out this problem. So Doug has a square window made up of 8 equal-sized panes of glass. Each pane has a height to width ratio of 5:2. There are borders around and between the panes that are 2 inches wide. The question is asking for the side length of the square windo... | [
"Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions.",
"This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and iteration to... | true |
Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and iteration to develop w... | Return your final response within \boxed{}. $P(x)$ is a polynomial of degree $3n$ such that
\begin{eqnarray*} P(0) = P(3) = \cdots &=& P(3n) = 2, \\ P(1) = P(4) = \cdots &=& P(3n-2) = 1, \\ P(2) = P(5) = \cdots &=& P(3n-1) = 0, \quad\text{ and }\\ && P(3n+1) = 730.\end{eqnarray*}
Determine $n$. | [
"Return your final response within \\boxed{}.",
"$P(x)$ is a polynomial of degree $3n$ such that",
"\\begin{eqnarray*} P(0) = P(3) = \\cdots &=& P(3n) = 2, \\\\",
"P(1) = P(4) = \\cdots &=& P(3n-2) = 1, \\\\",
"P(2) = P(5) = \\cdots &=& P(3n-1) = 0, \\quad\\text{ and }\\\\",
"&& P(3n+1) = 730.\\end{eqnarr... | <|begin_of_thought|>
Okay, let's see. I need to find the value of n given this polynomial P(x) of degree 3n that satisfies certain conditions at points 0, 1, 2, 3, ..., 3n, and also P(3n+1) = 730. Hmm, this seems a bit involved, but let me break it down step by step.
First, let me try to understand the problem. The po... | [
"<|begin_of_thought|>\nOkay, let's see. I need to find the value of n given this polynomial P(x) of degree 3n that satisfies certain conditions at points 0, 1, 2, 3, ..., 3n, and also P(3n+1) = 730. Hmm, this seems a bit involved, but let me break it down step by step.",
"First, let me try to understand the probl... | [
"Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions.",
"This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and iteration to... | true |
Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and iteration to develop w... | Return your final response within \boxed{}. Let $f$ be the function defined by $f(x)=ax^2-\sqrt{2}$ for some positive $a$. If $f(f(\sqrt{2}))=-\sqrt{2}$ then $a=$
$\text{(A) } \frac{2-\sqrt{2}}{2}\quad \text{(B) } \frac{1}{2}\quad \text{(C) } 2-\sqrt{2}\quad \text{(D) } \frac{\sqrt{2}}{2}\quad \text{(E) } \frac{2+\sqrt... | [
"Return your final response within \\boxed{}.",
"Let $f$ be the function defined by $f(x)=ax^2-\\sqrt{2}$ for some positive $a$.",
"If $f(f(\\sqrt{2}))=-\\sqrt{2}$ then $a=$",
"$\\text{(A) } \\frac{2-\\sqrt{2}}{2}\\quad$",
"$\\text{(B) } \\frac{1}{2}\\quad$",
"$\\text{(C) } 2-\\sqrt{2}\\quad$",
"$\\text... | <|begin_of_thought|>
Okay, let's try to figure out this problem step by step. The function is given as f(x) = a x² - √2, and we need to find the positive value of a such that f(f(√2)) = -√2. The answer choices are given, so maybe once we solve for a, we can match it with one of the options. Let me start by breaking dow... | [
"<|begin_of_thought|>\nOkay, let's try to figure out this problem step by step. The function is given as f(x) = a x² - √2, and we need to find the positive value of a such that f(f(√2)) = -√2. The answer choices are given, so maybe once we solve for a, we can match it with one of the options. Let me start by breaki... | [
"Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions.",
"This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and iteration to... | true |
"Your role as an assistant involves thoroughly exploring questions through a systematic long thinkin(...TRUNCATED) | "Return your final response within \\boxed{}. The total in-store price for an appliance is $\\textdo(...TRUNCATED) | ["Return your final response within \\boxed{}.","The total in-store price for an appliance is $\\tex(...TRUNCATED) | "<|begin_of_thought|>\nOkay, let's try to figure out this problem step by step. So, the question is (...TRUNCATED) | ["<|begin_of_thought|>\nOkay, let's try to figure out this problem step by step. So, the question is(...TRUNCATED) | ["Your role as an assistant involves thoroughly exploring questions through a systematic long thinki(...TRUNCATED) | true |
"Your role as an assistant involves thoroughly exploring questions through a systematic long thinkin(...TRUNCATED) | "Return your final response within \\boxed{}. Points $A,B,C,D,E$ and $F$ lie, in that order, on $\\o(...TRUNCATED) | ["Return your final response within \\boxed{}.","Points $A,B,C,D,E$ and $F$ lie, in that order, on $(...TRUNCATED) | "<|begin_of_thought|>\nOkay, let's try to tackle this geometry problem step by step. First, I need t(...TRUNCATED) | ["<|begin_of_thought|>\nOkay, let's try to tackle this geometry problem step by step. First, I need (...TRUNCATED) | ["Your role as an assistant involves thoroughly exploring questions through a systematic long thinki(...TRUNCATED) | true |
"Your role as an assistant involves thoroughly exploring questions through a systematic long thinkin(...TRUNCATED) | "Return your final response within \\boxed{}. During the softball season, Judy had $35$ hits. Among(...TRUNCATED) | ["Return your final response within \\boxed{}.","During the softball season, Judy had $35$ hits.","A(...TRUNCATED) | "<|begin_of_thought|>\nOkay, let's see. The problem is about Judy's hits during the softball season.(...TRUNCATED) | ["<|begin_of_thought|>\nOkay, let's see. The problem is about Judy's hits during the softball season(...TRUNCATED) | ["Your role as an assistant involves thoroughly exploring questions through a systematic long thinki(...TRUNCATED) | true |
"Your role as an assistant involves thoroughly exploring questions through a systematic long thinkin(...TRUNCATED) | "Return your final response within \\boxed{}. The graph, $G$ of $y=\\log_{10}x$ is rotated $90^{\\ci(...TRUNCATED) | ["Return your final response within \\boxed{}.","The graph, $G$ of $y=\\log_{10}x$ is rotated $90^{\(...TRUNCATED) | "<|begin_of_thought|>\nOkay, let's tackle this problem step by step. So, the question is about rotat(...TRUNCATED) | ["<|begin_of_thought|>\nOkay, let's tackle this problem step by step. So, the question is about rota(...TRUNCATED) | ["Your role as an assistant involves thoroughly exploring questions through a systematic long thinki(...TRUNCATED) | true |
"Your role as an assistant involves thoroughly exploring questions through a systematic long thinkin(...TRUNCATED) | "Return your final response within \\boxed{}. Jose, Thuy, and Kareem each start with the number 10. (...TRUNCATED) | ["Return your final response within \\boxed{}.","Jose, Thuy, and Kareem each start with the number 1(...TRUNCATED) | "<|begin_of_thought|>\nOkay, so I need to figure out who ends up with the largest final answer among(...TRUNCATED) | ["<|begin_of_thought|>\nOkay, so I need to figure out who ends up with the largest final answer amon(...TRUNCATED) | ["Your role as an assistant involves thoroughly exploring questions through a systematic long thinki(...TRUNCATED) | true |
"Your role as an assistant involves thoroughly exploring questions through a systematic long thinkin(...TRUNCATED) | "Return your final response within \\boxed{}. A set of consecutive positive integers beginning with (...TRUNCATED) | ["Return your final response within \\boxed{}.","A set of consecutive positive integers beginning wi(...TRUNCATED) | "<|begin_of_thought|>\nOkay, let me try to figure out this problem. So, we have a set of consecutive(...TRUNCATED) | ["<|begin_of_thought|>\nOkay, let me try to figure out this problem. So, we have a set of consecutiv(...TRUNCATED) | ["Your role as an assistant involves thoroughly exploring questions through a systematic long thinki(...TRUNCATED) | true |
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