id int64 0 999 | prompt listlengths 2 2 | completion listlengths 1 1 |
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0 | [
{
"content": "You are a skeleton-based reasoning model.\n\nWhen a question is given in a non-English language, you must first construct a reasoning skeleton (high-level plan) in English, and then use that skeleton to generate the full reasoning process and final answer in the same language as the original quest... | [
{
"content": "To prove the given inequality, we are given a function:\n\n$$\nf(x) = 1 - a \\cos x - b \\sin x - A \\cos 2x - B \\sin 2x\n$$\n\n그리고 모든 실수 x에 대해 $ f(x) \\geq 0 $인 조건.\n목표는 이 조건 하에 다음이 반드시 성립해야 한다는 것을 보여주는 것입니다.\n\n$$\na^2 + b^2 \\leq 2 \\quad \\text{and} \\quad A^2 + B^2 \\leq 1\n$$\n\n---\n\n### ... |
1 | [
{
"content": "You are a skeleton-based reasoning model.\n\nWhen a question is given in a non-English language, you must first construct a reasoning skeleton (high-level plan) in English, and then use that skeleton to generate the full reasoning process and final answer in the same language as the original quest... | [
{
"content": "문제를 해결하기 위해 0과 1 사이의 유리수를 찾는 것이 필요하며, 이 유리수를 가장 간단한 분수 $ \\frac{a}{b} $ 형태로 쓰면 분자와 분모의 곱이 $ 20! $이 되는 수를 찾는 것입니다.\n$.\n\n---\n\n### Step 1: 문제의 구조 이해\n\nA 0과 1 사이의 유리수는 최저 형태로 $ \\frac{a}{b} $로 쓸 수 있으며, 여기서:\n- $ 0 < a < b $\n- $ \\gcd(a, b) = 1 $ (즉, 분수는 최저 형태이다)\n\nThe product of the numerator a... |
2 | [
{
"content": "You are a skeleton-based reasoning model.\n\nWhen a question is given in a non-English language, you must first construct a reasoning skeleton (high-level plan) in English, and then use that skeleton to generate the full reasoning process and final answer in the same language as the original quest... | [
{
"content": "문제를 해결하기 위해 주어지는 무한차원 힐베르트 공간 $\\mathcal{H}$, 양의 상수 $d > 0$, 그리고 $\\mathcal{H}$ 내의 점들의 집합 $S$는 $S$ 내의 두 개의 서로 다른 점 사이의 거리가 정확히 $d$이다.\n우리는 $y \\in \\mathcal{H}$ such that the set가 존재함을 보여야 합니다.\n\n$$\n\\left\\{ \\frac{\\sqrt{2}}{d}(x - y) : x \\in S \\right\\}\n$$\n\n$\\mathcal{H}$에서 기저를 형성한다.\n\n... |
3 | [{"content":"You are a skeleton-based reasoning model.\n\nWhen a question is given in a non-English (...TRUNCATED) | [{"content":"제품의 나머지를 찾기 위해\n$$\n9 \\times 99 \\times 999 \\times \\cdots \\ti(...TRUNCATED) |
5 | [{"content":"You are a skeleton-based reasoning model.\n\nWhen a question is given in a non-English (...TRUNCATED) | [{"content":"르노(Rn)의 **평균 분자 속도**를 계산하기 위해서는 \"평균 분자 속(...TRUNCATED) |
6 | [{"content":"You are a skeleton-based reasoning model.\n\nWhen a question is given in a non-English (...TRUNCATED) | [{"content":"에너지가 저장된 두 캐피터가 **시리즈로 연결**되어 있을 때 **에(...TRUNCATED) |
7 | [{"content":"You are a skeleton-based reasoning model.\n\nWhen a question is given in a non-English (...TRUNCATED) | [{"content":"문제를 해결하기 위해 주어진 다각형은 다음과 같은 특성을 가집(...TRUNCATED) |
8 | [{"content":"You are a skeleton-based reasoning model.\n\nWhen a question is given in a non-English (...TRUNCATED) | [{"content":"### Summary of Solutions\n\n---\n\n### **문제 1**\n\n**Objective:**\n주어진 $ k $ (...TRUNCATED) |
9 | [{"content":"You are a skeleton-based reasoning model.\n\nWhen a question is given in a non-English (...TRUNCATED) | [{"content":"문제를 해결하기 위해 먼저 시나리오를 신중히 해석하고 주어진 (...TRUNCATED) |
10 | [{"content":"You are a skeleton-based reasoning model.\n\nWhen a question is given in a non-English (...TRUNCATED) | [{"content":"To determine the probability that Kathy will be happy, we must analyze the conditions u(...TRUNCATED) |
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