idx int64 0 2.72k | prompt stringlengths 885 11.1k | answers sequencelengths 32 32 | gt stringlengths 1 119 | true_reward bool 1
class |
|---|---|---|---|---|
1,800 | <|im_start|>system
You are a mathematical reasoning assistant. For each problem, follow these steps strictly:
1. Solve the problem using step-by-step reasoning and output the final answer within \boxed{}.
Always ensure clarity, correctness, and adherence to the required format.<|im_end|>
<|im_start|>user
Let $a, b, ... | [
"Let's check the value of the expression step by step. We know that \\( k = \\frac{a}{b} = 2 \\) and \\( m = \\frac{d}{a} = 2 \\). Therefore, we have \\( c = \\frac{bd}{a} = \\frac{b \\cdot a \\cdot 2}{a} = 2b \\) and \\( d = 2a \\).\n\nNow we need to evaluate \\( \\frac{a}{c} + \\frac{c}{a} + \\frac{b}{d} + \\frac... | 4 | false |
1,495 | <|im_start|>system
You are a mathematical reasoning assistant. For each problem, follow these steps strictly:
1. Solve the problem using step-by-step reasoning and output the final answer within \boxed{}.
Always ensure clarity, correctness, and adherence to the required format.<|im_end|>
<|im_start|>user
Let $\Delta ... | [
"The reasoning and calculations are correct, and the number of squares that can share two vertices with the isosceles right triangle is indeed 4. Therefore, the final answer is \\(\\boxed{4}\\).",
"To perform the self-evaluation, we need to verify the correctness of the reasoning and the final answer. Here's the ... | 6 | false |
308 | <|im_start|>system
You are a mathematical reasoning assistant. For each problem, follow these steps strictly:
1. Solve the problem using step-by-step reasoning and output the final answer within \boxed{}.
Always ensure clarity, correctness, and adherence to the required format.<|im_end|>
<|im_start|>user
Given the fu... | [
"The self-evaluation for the solution provided is:\n\\[\n\\boxed{[VERIFY] correct.}\n\\]",
"The reasoning provided indicates that the derivative \\(f'(x) = 3x^2 + 2x - a\\) must be non-negative for all \\(x\\). The minimum value of the quadratic expression \\(3x^2 + 2x - a\\) occurs at \\(x = -\\frac{1}{3}\\), an... | (-\infty, -\frac{1}{3}] | false |
1,611 | <|im_start|>system
You are a mathematical reasoning assistant. For each problem, follow these steps strictly:
1. Solve the problem using step-by-step reasoning and output the final answer within \boxed{}.
Always ensure clarity, correctness, and adherence to the required format.<|im_end|>
<|im_start|>user
Quadrilatera... | [
"Given:\n\n1. Quadrilateral $EFGH$ is a parallelogram.\n2. The measure of the external angle $EFG$ (formed by extending side $FG$) is $40^\\circ$.\n3. The measure of angle $F$ is $110^\\circ$.\n\nWe need to find the measure of angle $H$.\n\nSince $EFGH$ is a parallelogram, angle $H$ is opposite angle $F$. Therefore... | 40^\circ | false |
2,158 | <|im_start|>system
You are a mathematical reasoning assistant. For each problem, follow these steps strictly:
1. Solve the problem using step-by-step reasoning and output the final answer within \boxed{}.
Always ensure clarity, correctness, and adherence to the required format.<|im_end|>
<|im_start|>user
In rectangle... | [
"In the final answer, we have:\n\\[\nEF = \\frac{5\\sqrt{5}}{2}\n\\]\nThis can be verified using the calculations we performed.\n\nSo, the final answer is:\n\\(\\boxed{\\frac{5\\sqrt{5}}{2}}\\)\n```python\n# Calculation of EF using Python for verification\nfrom sympy import sqrt, Rational\n\n# Given values\nDE = Ra... | 10 | false |
2,358 | "<|im_start|>system\nYou are a mathematical reasoning assistant. For each problem, follow these step(...TRUNCATED) | ["You have provided a correct answer and reasoning, so the verification is as follows:\n\\[\n\\boxed(...TRUNCATED) | 11 | false |
2,438 | "<|im_start|>system\nYou are a mathematical reasoning assistant. For each problem, follow these step(...TRUNCATED) | ["To verify the correctness of our solution, let's break down the problem again and ensure that all (...TRUNCATED) | \frac{1}{2} | false |
1,096 | "<|im_start|>system\nYou are a mathematical reasoning assistant. For each problem, follow these step(...TRUNCATED) | ["Perform a self-evaluation:\n\n\\[\n\\boxed{103822}\n\\]\n\nLet's verify correctness. The final ans(...TRUNCATED) | 103682 | false |
2,315 | "<|im_start|>system\nYou are a mathematical reasoning assistant. For each problem, follow these step(...TRUNCATED) | ["Let's perform the self-evaluation. The final answer is $\\boxed{\\sqrt{65}}$. The reasoning and ca(...TRUNCATED) | \sqrt{51} | false |
237 | "<|im_start|>system\nYou are a mathematical reasoning assistant. For each problem, follow these step(...TRUNCATED) | ["You are a mathematical reasoning assistant. For each problem, follow these steps strictly:\n\n1. S(...TRUNCATED) | 7173 | false |
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