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values | reflection_prompt listlengths 2 2 | model_responses__mutated_prompts_reflection listlengths 1 1 | model_responses__mutated_prompts_reflection__finish_reason_length_flags listlengths 1 1 | model_responses__mutated_prompts_reflection__length_partial_responses listlengths 1 1 | reflection_prompt__mutated_prompts_reflection__metadata dict | model_responses__mutated_prompts_reflection__metadata dict |
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[
{
"from": "user",
"value": "## Task B-2.1.\n\nCalculate $\\left(\\frac{6+4 \\sqrt{2}}{\\sqrt{2}+\\sqrt{6+4 \\sqrt{2}}}+\\frac{6-4 \\sqrt{2}}{\\sqrt{2}-\\sqrt{6-4 \\sqrt{2}}}\\right)^{2}$."
},
{
"from": "assistant",
"value": "<think>\nOkay, so I have this expression to calculate, and then I need ... | ## Task B-2.1.
Calculate $\left(\frac{6+4 \sqrt{2}}{\sqrt{2}+\sqrt{6+4 \sqrt{2}}}+\frac{6-4 \sqrt{2}}{\sqrt{2}-\sqrt{6-4 \sqrt{2}}}\right)^{2}$. | null | null | [
{
"content": "You answer questions by saying \"Rewritten Question: \" then rewriting the question to only contain what is needed to solve it and then think step by step and then you give your final answer in \"<answer>\n(your answer)\n</answer>\". You always end with </answer>, you never ever end without giving... | 8 | {
"api_url": "http://10.32.36.236:9080/v1",
"backend": "litellm",
"chat_template_applied": true,
"generation_params": {
"chat_template_applied": true,
"max_tokens": 4096,
"n": 2,
"repetition_penalty": 1.1,
"temperature": 0.7,
"top_k": 20,
"top_p": 0.8
},
"model_name": "hosted_vll... | openthoughts | openthoughts | [
"Rewritten Question: Calculate $\\left(\\frac{6+4 \\sqrt{2}}{\\sqrt{2}+\\sqrt{6+4 \\sqrt{2}}} + \\frac{6-4 \\sqrt{2}}{\\sqrt{2}-\\sqrt{6-4 \\sqrt{2}}}\\right)^2$.\n\nStep 1: Simplify the expressions inside the parentheses.\nLet's denote $A = \\frac{6+4 \\sqrt{2}}{\\sqrt{2}+\\sqrt{6+4 \\sqrt{2}}}$ and $B = \\frac{6-... | [
false
] | [
"64"
] | rephrase | [
{
"content": "You think step by step and reflect on the given answer for the question reasoning about if the answer was correct or incorrect. You then always say <verdict>\ncorrect\n</verdict> or <verdict>\nincorrect\n</verdict> depending on if the answer was correct or incorrect in your opinion according to yo... | [
"Let us verify this answer... The model correctly identified that after rationalizing and simplifying the fractions, they both simplify to 4. Adding them together gives 8, and squaring 8 indeed results in 64.\n\n<verdict>\nCorrect\n</verdict>"
] | [
false
] | [
""
] | {
"api_url": "http://10.32.36.207:10080/v1",
"backend": "litellm",
"chat_template_applied": true,
"generation_params": {
"chat_template_applied": true,
"max_tokens": 512,
"n": 1,
"repetition_penalty": 1.1,
"temperature": 0.7,
"top_k": 20,
"top_p": 0.8
},
"model_name": "hosted_vll... | {
"backend": "litellm",
"model_name": "hosted_vllm/Qwen/Qwen2.5-7B-Instruct",
"n_responses": 1
} |
[
{
"from": "user",
"value": "## Task B-2.1.\n\nCalculate $\\left(\\frac{6+4 \\sqrt{2}}{\\sqrt{2}+\\sqrt{6+4 \\sqrt{2}}}+\\frac{6-4 \\sqrt{2}}{\\sqrt{2}-\\sqrt{6-4 \\sqrt{2}}}\\right)^{2}$."
},
{
"from": "assistant",
"value": "<think>\nOkay, so I have this expression to calculate, and then I need ... | ## Task B-2.1.
Calculate $\left(\frac{6+4 \sqrt{2}}{\sqrt{2}+\sqrt{6+4 \sqrt{2}}}+\frac{6-4 \sqrt{2}}{\sqrt{2}-\sqrt{6-4 \sqrt{2}}}\right)^{2}$. | null | null | [
{
"content": "You answer questions by saying \"Rewritten Question: \" then rewriting the question to only contain what is needed to solve it and then think step by step and then you give your final answer in \"<answer>\n(your answer)\n</answer>\". You always end with </answer>, you never ever end without giving... | 8 | {
"api_url": "http://10.32.36.236:9080/v1",
"backend": "litellm",
"chat_template_applied": true,
"generation_params": {
"chat_template_applied": true,
"max_tokens": 4096,
"n": 2,
"repetition_penalty": 1.1,
"temperature": 0.7,
"top_k": 20,
"top_p": 0.8
},
"model_name": "hosted_vll... | openthoughts | openthoughts | [
"Rewritten Question: Calculate $\\left(\\frac{6+4 \\sqrt{2}}{\\sqrt{2}+\\sqrt{6+4 \\sqrt{2}}} + \\frac{6-4 \\sqrt{2}}{\\sqrt{2}-\\sqrt{6-4 \\sqrt{2}}}\\right)^2$.\n\nStep 1: Simplify the expressions inside the parentheses.\nLet's first simplify the terms in the fractions.\n\nConsider the term $\\sqrt{6+4\\sqrt{2}}$... | [
false
] | [
"144"
] | rephrase | [
{
"content": "You think step by step and reflect on the given answer for the question reasoning about if the answer was correct or incorrect. You then always say <verdict>\ncorrect\n</verdict> or <verdict>\nincorrect\n</verdict> depending on if the answer was correct or incorrect in your opinion according to yo... | [
"Let us verify this answer... The rewritten question and subsequent steps taken by the model are accurate. The model correctly identified the need to simplify the radicals and used the appropriate algebraic manipulations to do so. It then proceeded to simplify the fractions and combine them appropriately. Finally, ... | [
false
] | [
""
] | {
"api_url": "http://10.32.36.207:10080/v1",
"backend": "litellm",
"chat_template_applied": true,
"generation_params": {
"chat_template_applied": true,
"max_tokens": 512,
"n": 1,
"repetition_penalty": 1.1,
"temperature": 0.7,
"top_k": 20,
"top_p": 0.8
},
"model_name": "hosted_vll... | {
"backend": "litellm",
"model_name": "hosted_vllm/Qwen/Qwen2.5-7B-Instruct",
"n_responses": 1
} |
[
{
"from": "user",
"value": "## Task B-2.1.\n\nCalculate $\\left(\\frac{6+4 \\sqrt{2}}{\\sqrt{2}+\\sqrt{6+4 \\sqrt{2}}}+\\frac{6-4 \\sqrt{2}}{\\sqrt{2}-\\sqrt{6-4 \\sqrt{2}}}\\right)^{2}$."
},
{
"from": "assistant",
"value": "<think>\nOkay, so I have this expression to calculate, and then I need ... | ## Task B-2.1.
Calculate $\left(\frac{6+4 \sqrt{2}}{\sqrt{2}+\sqrt{6+4 \sqrt{2}}}+\frac{6-4 \sqrt{2}}{\sqrt{2}-\sqrt{6-4 \sqrt{2}}}\right)^{2}$. | null | null | [
{
"content": "You answer questions by saying \"Rewritten Question: \" then rewriting the question to only contain what is needed to solve it and then think step by step and then you give your final answer in \"<answer>\n(your answer)\n</answer>\". You always end with </answer>, you never ever end without giving... | 8 | {
"api_url": "http://10.32.36.236:9080/v1",
"backend": "litellm",
"chat_template_applied": true,
"generation_params": {
"chat_template_applied": true,
"max_tokens": 4096,
"n": 2,
"repetition_penalty": 1.1,
"temperature": 0.7,
"top_k": 20,
"top_p": 0.8
},
"model_name": "hosted_vll... | openthoughts | openthoughts | [
"To solve the expression \\(\\left(\\frac{6+4 \\sqrt{2}}{\\sqrt{2}+\\sqrt{6+4 \\sqrt{2}}}+\\frac{6-4 \\sqrt{2}}{\\sqrt{2}-\\sqrt{6-4 \\sqrt{2}}}\\right)^{2}\\), we will first simplify the terms inside the parentheses.\n\n### Step 1: Simplify Each Fraction\n\n#### First Term:\nLet's consider the term \\(\\frac{6+4 \... | [
false
] | [
"4"
] | alternative | [
{
"content": "You think step by step and reflect on the given answer for the question reasoning about if the answer was correct or incorrect. You then always say <verdict>\ncorrect\n</verdict> or <verdict>\nincorrect\n</verdict> depending on if the answer was correct or incorrect in your opinion according to yo... | [
"Let us verify this answer... Upon reviewing the detailed solution provided, it appears there was a miscalculation towards the final simplified form. While the intermediate steps were correctly handled, the final squared term simplification led to an incorrect conclusion. Based on the detailed breakdown, the correc... | [
false
] | [
""
] | {
"api_url": "http://10.32.36.207:10080/v1",
"backend": "litellm",
"chat_template_applied": true,
"generation_params": {
"chat_template_applied": true,
"max_tokens": 512,
"n": 1,
"repetition_penalty": 1.1,
"temperature": 0.7,
"top_k": 20,
"top_p": 0.8
},
"model_name": "hosted_vll... | {
"backend": "litellm",
"model_name": "hosted_vllm/Qwen/Qwen2.5-7B-Instruct",
"n_responses": 1
} |
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false
] | [
"9"
] | alternative | [{"content":"You think step by step and reflect on the given answer for the question reasoning about(...TRUNCATED) | ["Let us verify this answer... The model response correctly identifies the values of the radicals, s(...TRUNCATED) | [
false
] | [
""
] | {"api_url":"http://10.32.36.207:10080/v1","backend":"litellm","chat_template_applied":true,"generati(...TRUNCATED) | {
"backend": "litellm",
"model_name": "hosted_vllm/Qwen/Qwen2.5-7B-Instruct",
"n_responses": 1
} |
[{"from":"user","value":"8. Given six points in space $A, B, C, D, E, F$ with no four points being c(...TRUNCATED) | "8. Given six points in space $A, B, C, D, E, F$ with no four points being coplanar. Then the maximu(...TRUNCATED) | null | null | [{"content":"You answer questions by saying \"Rewritten Question: \" then rewriting the question to (...TRUNCATED) | 12 | {"api_url":"http://10.32.36.236:9080/v1","backend":"litellm","chat_template_applied":true,"generatio(...TRUNCATED) | openthoughts | openthoughts | ["Rewritten Question: Six points in space with no four points coplanar. Find the maximum number of l(...TRUNCATED) | [
true
] | [
"12"
] | rephrase | [{"content":"You think step by step and reflect on the given answer for the question reasoning about(...TRUNCATED) | ["Let us verify this answer... The original problem involves finding the maximum number of line segm(...TRUNCATED) | [
false
] | [
""
] | {"api_url":"http://10.32.36.207:10080/v1","backend":"litellm","chat_template_applied":true,"generati(...TRUNCATED) | {
"backend": "litellm",
"model_name": "hosted_vllm/Qwen/Qwen2.5-7B-Instruct",
"n_responses": 1
} |
[{"from":"user","value":"8. Given six points in space $A, B, C, D, E, F$ with no four points being c(...TRUNCATED) | "8. Given six points in space $A, B, C, D, E, F$ with no four points being coplanar. Then the maximu(...TRUNCATED) | null | null | [{"content":"You answer questions by saying \"Rewritten Question: \" then rewriting the question to (...TRUNCATED) | 12 | {"api_url":"http://10.32.36.236:9080/v1","backend":"litellm","chat_template_applied":true,"generatio(...TRUNCATED) | openthoughts | openthoughts | ["Rewritten Question: Six points in space with no four points being coplanar. Find the maximum numbe(...TRUNCATED) | [
false
] | [
"9"
] | rephrase | [{"content":"You think step by step and reflect on the given answer for the question reasoning about(...TRUNCATED) | ["Let us verify this answer... The original problem asks for the maximum number of line segments tha(...TRUNCATED) | [
false
] | [
""
] | {"api_url":"http://10.32.36.207:10080/v1","backend":"litellm","chat_template_applied":true,"generati(...TRUNCATED) | {
"backend": "litellm",
"model_name": "hosted_vllm/Qwen/Qwen2.5-7B-Instruct",
"n_responses": 1
} |
[{"from":"user","value":"8. Given six points in space $A, B, C, D, E, F$ with no four points being c(...TRUNCATED) | "8. Given six points in space $A, B, C, D, E, F$ with no four points being coplanar. Then the maximu(...TRUNCATED) | null | null | [{"content":"You answer questions by saying \"Rewritten Question: \" then rewriting the question to (...TRUNCATED) | 12 | {"api_url":"http://10.32.36.236:9080/v1","backend":"litellm","chat_template_applied":true,"generatio(...TRUNCATED) | openthoughts | openthoughts | ["Rewritten Question: Given six points in space with no four points being coplanar, find the maximum(...TRUNCATED) | [
true
] | [
"12"
] | rephrase | [{"content":"You think step by step and reflect on the given answer for the question reasoning about(...TRUNCATED) | ["Let us verify this answer. The model correctly identifies the application of Turán's theorem to a(...TRUNCATED) | [
false
] | [
""
] | {"api_url":"http://10.32.36.207:10080/v1","backend":"litellm","chat_template_applied":true,"generati(...TRUNCATED) | {
"backend": "litellm",
"model_name": "hosted_vllm/Qwen/Qwen2.5-7B-Instruct",
"n_responses": 1
} |
[{"from":"user","value":"8. Given six points in space $A, B, C, D, E, F$ with no four points being c(...TRUNCATED) | "8. Given six points in space $A, B, C, D, E, F$ with no four points being coplanar. Then the maximu(...TRUNCATED) | null | null | [{"content":"You answer questions by saying \"Rewritten Question: \" then rewriting the question to (...TRUNCATED) | 12 | {"api_url":"http://10.32.36.236:9080/v1","backend":"litellm","chat_template_applied":true,"generatio(...TRUNCATED) | openthoughts | openthoughts | ["Rewritten Question: Six points in space with no four points being coplanar. Find the maximum numbe(...TRUNCATED) | [
true
] | [
"12"
] | rephrase | [{"content":"You think step by step and reflect on the given answer for the question reasoning about(...TRUNCATED) | ["Let us verify this answer. The model response correctly identifies that the problem involves avoid(...TRUNCATED) | [
false
] | [
""
] | {"api_url":"http://10.32.36.207:10080/v1","backend":"litellm","chat_template_applied":true,"generati(...TRUNCATED) | {
"backend": "litellm",
"model_name": "hosted_vllm/Qwen/Qwen2.5-7B-Instruct",
"n_responses": 1
} |
[{"from":"user","value":"8. Given six points in space $A, B, C, D, E, F$ with no four points being c(...TRUNCATED) | "8. Given six points in space $A, B, C, D, E, F$ with no four points being coplanar. Then the maximu(...TRUNCATED) | null | null | [{"content":"You answer questions by saying \"Rewritten Question: \" then rewriting the question to (...TRUNCATED) | 12 | {"api_url":"http://10.32.36.236:9080/v1","backend":"litellm","chat_template_applied":true,"generatio(...TRUNCATED) | openthoughts | openthoughts | ["To determine the maximum number of line segments (edges) that can be drawn among six points \\( A,(...TRUNCATED) | [
true
] | [
"12"
] | alternative | [{"content":"You think step by step and reflect on the given answer for the question reasoning about(...TRUNCATED) | ["Let us verify this answer. The original question asks for the maximum number of line segments that(...TRUNCATED) | [
false
] | [
""
] | {"api_url":"http://10.32.36.207:10080/v1","backend":"litellm","chat_template_applied":true,"generati(...TRUNCATED) | {
"backend": "litellm",
"model_name": "hosted_vllm/Qwen/Qwen2.5-7B-Instruct",
"n_responses": 1
} |
[{"from":"user","value":"8. Given six points in space $A, B, C, D, E, F$ with no four points being c(...TRUNCATED) | "8. Given six points in space $A, B, C, D, E, F$ with no four points being coplanar. Then the maximu(...TRUNCATED) | null | null | [{"content":"You answer questions by saying \"Rewritten Question: \" then rewriting the question to (...TRUNCATED) | 12 | {"api_url":"http://10.32.36.236:9080/v1","backend":"litellm","chat_template_applied":true,"generatio(...TRUNCATED) | openthoughts | openthoughts | ["To determine the maximum number of line segments (edges) that can be drawn among six points such t(...TRUNCATED) | [
false
] | [
"9"
] | alternative | [{"content":"You think step by step and reflect on the given answer for the question reasoning about(...TRUNCATED) | ["Let us verify this answer. The original question asks for the maximum number of line segments that(...TRUNCATED) | [
false
] | [
""
] | {"api_url":"http://10.32.36.207:10080/v1","backend":"litellm","chat_template_applied":true,"generati(...TRUNCATED) | {
"backend": "litellm",
"model_name": "hosted_vllm/Qwen/Qwen2.5-7B-Instruct",
"n_responses": 1
} |
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