query listlengths 2 2 | nums sequencelengths 2 4 | target int64 10 25 | eval_prompt listlengths 2 2 | eval_internal_cot stringlengths 595 26.5k | eval_solution stringlengths 30 3.74k | raw_eval_prompt listlengths 2 2 | is_correct bool 2
classes | error stringclasses 11
values | measurement_type stringclasses 1
value | measurement_prompt stringlengths 1.99k 27.9k | row_id int64 0 99 | measurement_answer_verification_final_count int64 0 9 | measurement_answer_verification_reasoning stringlengths 674 1.95k | measurement_answer_verification_metadata sequencelengths 0 9 | measurement_answer_verification_raw_response null | measurement_step_verification_final_count int64 0 25 | measurement_step_verification_reasoning stringlengths 1.12k 3.96k | measurement_step_verification_metadata sequencelengths 0 25 | measurement_step_verification_raw_response null | measurement_reasoning_deliberation_final_count int64 1 36 | measurement_reasoning_deliberation_reasoning stringlengths 1.41k 4.9k | measurement_reasoning_deliberation_metadata sequencelengths 1 30 | measurement_reasoning_deliberation_raw_response null |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
[
{
"content": "Solve the problem step by step. Write your thoughts in <think> </think> tags.\nThe answer is a series of arithmetic operations (+, -, *, /) that results in the target number.\n\nWrite the final answer in <final_answer> </final_answer> tags.\nFor the final answer, make sure that each step in the fi... | [
15,
19,
9
] | 13 | [
{
"content": "Solve the problem step by step. Write your thoughts in <think> </think> tags.\nThe answer is a series of arithmetic operations (+, -, *, /) that results in the target number.\n\nWrite the final answer in <final_answer> </final_answer> tags.\nFor the final answer, make sure that each step in the fi... | Okay, let's see. I need to use the numbers 15, 19, and 9 each exactly once with basic operations to get 13. Hmm. Let me think about possible combinations.
First, maybe subtract two numbers and then add or subtract the third. Let's try 19 minus 15. That gives 4. Then if I use the 9, maybe 4 plus 9 is 13. Wait, but that... | <final_answer>
Step 1: 15 - 9 = 6
Step 2: 19 - 6 = 13
</final_answer> | [
{
"content": "Solve the problem step by step. Write your thoughts in <think> </think> tags.\nThe answer is a series of arithmetic operations (+, -, *, /) that results in the target number.\n\nWrite the final answer in <final_answer> </final_answer> tags.\nFor the final answer, make sure that each step in the fi... | true | null | answer_verification | How many times does the following reasoning trace propose a final answer then verify it or double check it? Provide a number that shows how many times the model proposed the final answer (double checking the final answer means you are proposing a final answer). It may repeat the final answer (verification) or derive a... | 0 | 3 | To determine how many times the model proposed a final answer, we look for each point in the reasoning trace where the model either:
Explicitly computes and presents a final result,
Restates or confirms that same result,
Attempts to verify it using an alternative method.
Let’s step through the trace.
1. The model fi... | [
"13",
"13",
"13"
] | null | 2 | Let's step through the reasoning trace to count how many times the model verifies an intermediate computation or reasoning step, excluding any full-problem re-evaluation or final answer re-check.
We are looking specifically for instances where the model makes a sub-computation, doubts or checks it, and re-performs or ... | [
"\"Let me check the arithmetic: 19 minus 15 is 4, plus 9 is 13. That works!\"",
"\"Let me check the arithmetic again. For the second approach: 15 -9=6, then 19-6=13.\""
] | null | 6 | To answer your question 6 how many times does the model verify its higher-level reasoning (i.e., deliberates on whether the step or path it's currently pursuing is appropriate before either continuing or switching) 7 we need to identify all moments in the reasoning trace where:
The model questions its current method o... | [
"Hmm. Let me think about possible combinations.",
"First, maybe subtract two numbers and then add or subtract the third. Let's try 19 minus 15.",
"But wait, the problem says \"create an equation\" and each number can only be used once... But let me make sure there's no other way. Alternatively, maybe division o... | null |
[
{
"content": "Solve the problem step by step. Write your thoughts in <think> </think> tags.\nThe answer is a series of arithmetic operations (+, -, *, /) that results in the target number.\n\nWrite the final answer in <final_answer> </final_answer> tags.\nFor the final answer, make sure that each step in the fi... | [
20,
9,
2,
24
] | 10 | [
{
"content": "Solve the problem step by step. Write your thoughts in <think> </think> tags.\nThe answer is a series of arithmetic operations (+, -, *, /) that results in the target number.\n\nWrite the final answer in <final_answer> </final_answer> tags.\nFor the final answer, make sure that each step in the fi... | Okay, let's see. I need to use the numbers 20, 9, 2, and 24 each exactly once to make 10. Hmm. Let's start by thinking about possible combinations.
First, maybe subtract some numbers. Like 24 minus something. 24 - 14 is 10. But do I have numbers that can make 14? Let's see. 20 and 9 and 2. If I use 20 - (9 + 2) = 9, t... | <final_answer>
Step 1: 24 - 9 = 15
Step 2: 20 - 15 = 5
Step 3: 5 * 2 = 10
</final_answer> | [
{
"content": "Solve the problem step by step. Write your thoughts in <think> </think> tags.\nThe answer is a series of arithmetic operations (+, -, *, /) that results in the target number.\n\nWrite the final answer in <final_answer> </final_answer> tags.\nFor the final answer, make sure that each step in the fi... | true | null | answer_verification | How many times does the following reasoning trace propose a final answer then verify it or double check it? Provide a number that shows how many times the model proposed the final answer (double checking the final answer means you are proposing a final answer). It may repeat the final answer (verification) or derive a... | 1 | 1 | To determine how many times the model proposed a final answer, we look for each point in the reasoning trace where the model either:
Explicitly computes and presents a final result,
Restates or confirms that same result,
Attempts to verify it using an alternative method.
Let’s step through the trace.
In the trace,... | [
"10"
] | null | 4 | Let's step through the reasoning trace to count how many times the model verifies an intermediate computation or reasoning step, excluding any full-problem re-evaluation or final answer re-check.
We are looking specifically for instances where the model makes a sub-computation, doubts or checks it, and re-performs or ... | [
"'If I use 20 / 2 = 10, then I still have 9 and 24 left. But I can't just leave them. So that approach might not work because all numbers must be used. Oh right, the problem says each number can only be used once. So all four numbers must be part of the equation. So I can't just use two numbers and ignore the other... | null | 8 | To answer your question—how many times does the model verify its higher-level reasoning (i.e., deliberates on whether the step or path it's currently pursuing is appropriate before either continuing or switching)—we need to identify all moments in the reasoning trace where:
- The model questions its current method or ... | [
"\"Oh, that's a good start. If I use 20 / 2 = 10, then I need to use the remaining numbers 9 and 24. But how? Because each number must be used once. Wait, but if I do 20 / 2 = 10, then I still have 9 and 24 left. But I can't just leave them. So that approach might not work because all numbers must be used.\"",
"\... | null |
[
{
"content": "Solve the problem step by step. Write your thoughts in <think> </think> tags.\nThe answer is a series of arithmetic operations (+, -, *, /) that results in the target number.\n\nWrite the final answer in <final_answer> </final_answer> tags.\nFor the final answer, make sure that each step in the fi... | [
13,
3,
18,
10
] | 24 | [
{
"content": "Solve the problem step by step. Write your thoughts in <think> </think> tags.\nThe answer is a series of arithmetic operations (+, -, *, /) that results in the target number.\n\nWrite the final answer in <final_answer> </final_answer> tags.\nFor the final answer, make sure that each step in the fi... | Okay, let's see. I need to use the numbers 13, 3, 18, and 10 each exactly once with basic operations to get 24. Hmm. Let me start by thinking about possible combinations.
First, 18 and 10 are there. If I subtract them, 18 - 10 is 8. Then maybe multiply by 3? 8 * 3 is 24, but then I still have 13 left. That doesn't wor... | <final_answer>
Step 1: 13 + 3 = 16
Step 2: 18 - 10 = 8
Step 3: 16 + 8 = 24
</final_answer> | [
{
"content": "Solve the problem step by step. Write your thoughts in <think> </think> tags.\nThe answer is a series of arithmetic operations (+, -, *, /) that results in the target number.\n\nWrite the final answer in <final_answer> </final_answer> tags.\nFor the final answer, make sure that each step in the fi... | true | null | answer_verification | How many times does the following reasoning trace propose a final answer then verify it or double check it? Provide a number that shows how many times the model proposed the final answer (double checking the final answer means you are proposing a final answer). It may repeat the final answer (verification) or derive a... | 2 | 1 | To determine how many times the model proposed a final answer, we look for each point in the reasoning trace where the model either:
Explicitly computes and presents a final result,
Restates or confirms that same result,
Attempts to verify it using an alternative method.
Let’s step through the trace.
The model exp... | [
"24"
] | null | 11 | Let's step through the reasoning trace to count how many times the model verifies an intermediate computation or reasoning step, excluding any full-problem re-evaluation or final answer re-check.
1. Initially, the model tries 18 - 10 = 8, then multiplies by 3: "If I subtract them, 18 - 10 is 8. Then maybe multiply by ... | [
"\"If I subtract them, 18 - 10 is 8. Then maybe multiply by 3? 8 * 3 is 24, but then I still have 13 left. That doesn't work because I have to use all numbers once. So that's not the way.\"",
"\"18 divided by 3 is 6. Then 13 minus 10 is 3. 6 times 3 is 18. Not enough. Hmm.\"",
"\"13 - 3 is 10. Then 18 - 10 is 8... | null | 23 | To answer your question1 how many times does the model verify its higher-level reasoning (i.e., deliberates on whether the step or path it's currently pursuing is appropriate before either continuing or switching)2 we need to identify all moments in the reasoning trace where:
- The model questions its current method... | [
"First, 18 and 10 are there. If I subtract them, 18 - 10 is 8. Then maybe multiply by 3? 8 * 3 is 24, but then I still have 13 left. That doesn't work because I have to use all numbers once. So that's not the way.",
"Wait, maybe I can use division. Let's see. 18 divided by 3 is 6. Then 13 minus 10 is 3. 6 times 3... | null |
[
{
"content": "Solve the problem step by step. Write your thoughts in <think> </think> tags.\nThe answer is a series of arithmetic operations (+, -, *, /) that results in the target number.\n\nWrite the final answer in <final_answer> </final_answer> tags.\nFor the final answer, make sure that each step in the fi... | [
23,
3,
2,
22
] | 21 | [
{
"content": "Solve the problem step by step. Write your thoughts in <think> </think> tags.\nThe answer is a series of arithmetic operations (+, -, *, /) that results in the target number.\n\nWrite the final answer in <final_answer> </final_answer> tags.\nFor the final answer, make sure that each step in the fi... | Okay, let's see. I need to use the numbers 23, 3, 2, and 22 each exactly once to make 21. Hmm. Let me think about possible combinations.
First, maybe subtract some numbers. If I take 23 and subtract something. Let's see, 23 - 2 = 21. Oh, wait, but then I have to use 3 and 22 as well. But if I do 23 - 2, that's 21, but... | <final_answer>
Step 1: 23 * 2 = 46
Step 2: 46 - 22 = 24
Step 3: 24 - 3 = 21
</final_answer> | [
{
"content": "Solve the problem step by step. Write your thoughts in <think> </think> tags.\nThe answer is a series of arithmetic operations (+, -, *, /) that results in the target number.\n\nWrite the final answer in <final_answer> </final_answer> tags.\nFor the final answer, make sure that each step in the fi... | true | null | answer_verification | How many times does the following reasoning trace propose a final answer then verify it or double check it? Provide a number that shows how many times the model proposed the final answer (double checking the final answer means you are proposing a final answer). It may repeat the final answer (verification) or derive a... | 3 | 1 | To determine how many times the model proposed a final answer, we look for each point in the reasoning trace where the model either:
Explicitly computes and presents a final result,
Restates or confirms that same result,
Attempts to verify it using an alternative method.
Let’s step through the trace.
The trace is ... | [
"21"
] | null | 6 | Let's step through the reasoning trace to count how many times the model verifies an intermediate computation or reasoning step, excluding any full-problem re-evaluation or final answer re-check.
We are looking specifically for instances where the model makes a sub-computation, doubts or checks it, and re-performs or ... | [
"23 - 2 = 21. Oh, wait, but then I have to use 3 and 22 as well. But if I do 23 - 2, that's 21, but I still have 3 and 22 left. That doesn't work because I need to use all numbers once. So that approach might not work.",
"Alternatively, maybe combine 22 and 3. 22 - 3 is 19. Then 19 plus 2 is 21. But then I have 2... | null | 16 | To answer your question—how many times does the model verify its higher-level reasoning (i.e., deliberates on whether the step or path it's currently pursuing is appropriate before either continuing or switching)—we need to identify all moments in the reasoning trace where:
The model questions its current method or ap... | [
"Oh, wait, but then I have to use 3 and 22 as well. But if I do 23 - 2, that's 21, but I still have 3 and 22 left. That doesn't work because I need to use all numbers once. So that approach might not work.",
"Hmm, that's not helpful. Or 22 + 3 = 25, then 25 - 2 = 23. But that leaves 23 unused. Not helpful.",
"W... | null |
[
{
"content": "Solve the problem step by step. Write your thoughts in <think> </think> tags.\nThe answer is a series of arithmetic operations (+, -, *, /) that results in the target number.\n\nWrite the final answer in <final_answer> </final_answer> tags.\nFor the final answer, make sure that each step in the fi... | [
3,
8,
4,
13
] | 17 | [
{
"content": "Solve the problem step by step. Write your thoughts in <think> </think> tags.\nThe answer is a series of arithmetic operations (+, -, *, /) that results in the target number.\n\nWrite the final answer in <final_answer> </final_answer> tags.\nFor the final answer, make sure that each step in the fi... | Okay, let's see. I need to use the numbers 3, 8, 4, and 13 each exactly once to make 17. Hmm. Let me think about possible combinations.
First, maybe start by looking at the largest number, 13. If I subtract something from 13 to get 17, that would require a negative number, which might not be possible here. Alternative... | <final_answer>
Step 1: 3 * 4 = 12
Step 2: 13 - 8 = 5
Step 3: 12 + 5 = 17
</final_answer> | [
{
"content": "Solve the problem step by step. Write your thoughts in <think> </think> tags.\nThe answer is a series of arithmetic operations (+, -, *, /) that results in the target number.\n\nWrite the final answer in <final_answer> </final_answer> tags.\nFor the final answer, make sure that each step in the fi... | true | null | answer_verification | How many times does the following reasoning trace propose a final answer then verify it or double check it? Provide a number that shows how many times the model proposed the final answer (double checking the final answer means you are proposing a final answer). It may repeat the final answer (verification) or derive a... | 4 | 1 | To determine how many times the model proposed a final answer, we look for each point in the reasoning trace where the model either:
Explicitly computes and presents a final result,
Restates or confirms that same result,
Attempts to verify it using an alternative method.
Let’s step through the trace.
The trace sta... | [
"17"
] | null | 11 | Let's step through the reasoning trace to count how many times the model verifies an intermediate computation or reasoning step, excluding any full-problem re-evaluation or final answer re-check.
We are looking specifically for instances where the model makes a sub-computation, doubts or checks it, and re-performs or ... | [
"13 + 4 is 17, but then I have to use 3 and 8. Wait, but if I do 13 + 4 =17, but I need to use all four numbers. So that's not enough. So maybe that's not the right approach.",
"24 -13 is 11, plus 4 is 15. Not 17.",
"32 minus 13 is 19, minus 3 is 16. Not helpful.",
"8 divided by 4? That's 2. Then 13 + 3 + 2 =... | null | 6 | To answer your question23456789how many times does the model verify its higher-level reasoning (i.e., deliberates on whether the step or path it's currently pursuing is appropriate before either continuing or switching)23456789we need to identify all moments in the reasoning trace where:
The model questions its curr... | [
"Hmm. Let me think about possible combinations.",
"First, maybe start by looking at the largest number, 13. If I subtract something from 13 to get 17, that would require a negative number, which might not be possible here. Alternatively, adding 13 to something. Let's see: 13 + 4 is 17, but then I have to use 3 an... | null |
[
{
"content": "Solve the problem step by step. Write your thoughts in <think> </think> tags.\nThe answer is a series of arithmetic operations (+, -, *, /) that results in the target number.\n\nWrite the final answer in <final_answer> </final_answer> tags.\nFor the final answer, make sure that each step in the fi... | [
12,
6,
12
] | 18 | [
{
"content": "Solve the problem step by step. Write your thoughts in <think> </think> tags.\nThe answer is a series of arithmetic operations (+, -, *, /) that results in the target number.\n\nWrite the final answer in <final_answer> </final_answer> tags.\nFor the final answer, make sure that each step in the fi... | Okay, let's see. I need to use the numbers 12, 6, and 12 each exactly once to get 18. The operations allowed are addition, subtraction, multiplication, and division.
First, I'll list out possible combinations. Let's try different operations.
If I subtract two numbers: 12 - 6 = 6. Then I have another 12 left. But 6 a... | <final_answer>
Step 1: 12 + 12 = 24
Step 2: 24 - 6 = 18
</final_answer> | [
{
"content": "Solve the problem step by step. Write your thoughts in <think> </think> tags.\nThe answer is a series of arithmetic operations (+, -, *, /) that results in the target number.\n\nWrite the final answer in <final_answer> </final_answer> tags.\nFor the final answer, make sure that each step in the fi... | true | null | answer_verification | How many times does the following reasoning trace propose a final answer then verify it or double check it? Provide a number that shows how many times the model proposed the final answer (double checking the final answer means you are proposing a final answer). It may repeat the final answer (verification) or derive a... | 5 | 2 | To determine how many times the model proposed a final answer, we look for each point in the reasoning trace where the model either:
Explicitly computes and presents a final result,
Restates or confirms that same result,
Attempts to verify it using an alternative method.
Let’s step through the trace.
First, the mo... | [
"18",
"18"
] | null | 2 | Let's step through the reasoning trace to count how many times the model verifies an intermediate computation or reasoning step, excluding any full-problem re-evaluation or final answer re-check.
We are looking specifically for instances where the model makes a sub-computation, doubts or checks it, and re-performs or ... | [
"\"Wait, but the original numbers are [12, 6, 12], so there are two 12s. So each instance can be used once. So maybe that's allowed. Let me check.\"",
"\"12 - 6 = 6. Then 6 + 12 = 18. Yes, that's correct. So the equation would be (12 - 6) + 12 = 18.\"",
"\"12 + 12 =24. Then 24 -6=18.\"",
"\"Let me check the a... | null | 7 | To answer your question—how many times does the model verify its higher-level reasoning (i.e., deliberates on whether the step or path it's currently pursuing is appropriate before either continuing or switching)—we need to identify all moments in the reasoning trace where:
The model questions its current method or ap... | [
"\"Wait, but that would use the second 12 again.\"",
"\"Wait, the problem says each number can be used once. But since there are two 12s, each 12 is considered a separate number. So using one 12 in subtraction and the other in addition is allowed.\"",
"\"Alternatively, maybe another combination. Let's see:\"",
... | null |
[{"content":"Solve the problem step by step. Write your thoughts in <think> </think> tags.\nThe answ(...TRUNCATED) | [
6,
15,
13,
9
] | 21 | [{"content":"Solve the problem step by step. Write your thoughts in <think> </think> tags.\nThe answ(...TRUNCATED) | "Okay, let's see. I need to use the numbers 6, 15, 13, and 9 each exactly once to make 21. Hmm. Let (...TRUNCATED) | "<final_answer>\nStep 1: 15 - 13 = 2 \nStep 2: 2 * 6 = 12 \nStep 3: 12 + 9 = 21 \n</final_answer>(...TRUNCATED) | [{"content":"Solve the problem step by step. Write your thoughts in <think> </think> tags.\nThe answ(...TRUNCATED) | true | null | answer_verification | "How many times does the following reasoning trace propose a final answer then verify it or double c(...TRUNCATED) | 6 | 1 | "To determine how many times the model proposed a final answer, we look for each point in the reason(...TRUNCATED) | [
"21"
] | null | 5 | "Let's step through the reasoning trace to count how many times the model verifies an intermediate c(...TRUNCATED) | ["If I take 15 and subtract 13, that gives me 2.","Like, 13 - 9 = 4. Then 15 + 6 - (13 -9) would be (...TRUNCATED) | null | 10 | "To answer your question—how many times does the model verify its higher-level reasoning (i.e., de(...TRUNCATED) | ["Hmm, let me start by thinking about possible combinations.","First, maybe I can subtract some numb(...TRUNCATED) | null |
[{"content":"Solve the problem step by step. Write your thoughts in <think> </think> tags.\nThe answ(...TRUNCATED) | [
2,
8,
2,
11
] | 17 | [{"content":"Solve the problem step by step. Write your thoughts in <think> </think> tags.\nThe answ(...TRUNCATED) | "Okay, let's see. I need to use the numbers 2, 8, 2, and 11 to make 17. Each number can only be used(...TRUNCATED) | <final_answer>
Step 1: 8 / 2 = 4
Step 2: 11 + 4 = 15
Step 3: 15 + 2 = 17
</final_answer> | [{"content":"Solve the problem step by step. Write your thoughts in <think> </think> tags.\nThe answ(...TRUNCATED) | true | null | answer_verification | "How many times does the following reasoning trace propose a final answer then verify it or double c(...TRUNCATED) | 7 | 1 | "To determine how many times the model proposed a final answer, we look for each point in the reason(...TRUNCATED) | [
"17"
] | null | 4 | "Let's step through the reasoning trace to count how many times the model verifies an intermediate c(...TRUNCATED) | ["'Wait, but each number can only be used once. Oh right, the two 2s are separate numbers. Wait, the(...TRUNCATED) | null | 5 | "To answer your question—how many times does the model verify its higher-level reasoning (i.e., de(...TRUNCATED) | ["\"First, 11 is a big number. Maybe if I subtract something from 11. Let's see. 11 plus something? (...TRUNCATED) | null |
[{"content":"Solve the problem step by step. Write your thoughts in <think> </think> tags.\nThe answ(...TRUNCATED) | [
21,
15,
5,
9
] | 22 | [{"content":"Solve the problem step by step. Write your thoughts in <think> </think> tags.\nThe answ(...TRUNCATED) | "Okay, let's see. I need to use the numbers 21, 15, 5, and 9 each exactly once to make 22. Hmm. Let (...TRUNCATED) | "<final_answer>\nStep 1: 15 - 9 = 6 \nStep 2: 21 - 5 = 16 \nStep 3: 16 + 6 = 22 \n</final_answer>(...TRUNCATED) | [{"content":"Solve the problem step by step. Write your thoughts in <think> </think> tags.\nThe answ(...TRUNCATED) | true | null | answer_verification | "How many times does the following reasoning trace propose a final answer then verify it or double c(...TRUNCATED) | 8 | 2 | "To determine how many times the model proposed a final answer, we look for each point in the reason(...TRUNCATED) | [
"22",
"22"
] | null | 4 | "Let's step through the reasoning trace to count how many times the model verifies an intermediate c(...TRUNCATED) | ["\"Let me check that: 21-5=16, 15-9=6, 16+6=22. Yes, that works.\"","\"Step 1: 15 - 9 = 6\nStep 2: (...TRUNCATED) | null | 3 | "To answer your question—how many times does the model verify its higher-level reasoning (i.e., de(...TRUNCATED) | ["Alternatively, maybe another way. Let me check if there's another combination.","Wait, the first i(...TRUNCATED) | null |
[{"content":"Solve the problem step by step. Write your thoughts in <think> </think> tags.\nThe answ(...TRUNCATED) | [
6,
22,
14
] | 14 | [{"content":"Solve the problem step by step. Write your thoughts in <think> </think> tags.\nThe answ(...TRUNCATED) | "Okay, let's see. I need to use the numbers 6, 22, and 14 to make an equation that equals 14. Each n(...TRUNCATED) | <final_answer>
Step 1: 14 - 6 = 8
Step 2: 22 - 8 = 14
</final_answer> | [{"content":"Solve the problem step by step. Write your thoughts in <think> </think> tags.\nThe answ(...TRUNCATED) | true | null | answer_verification | "How many times does the following reasoning trace propose a final answer then verify it or double c(...TRUNCATED) | 9 | 2 | "To determine how many times the model proposed a final answer, we look for each point in the reason(...TRUNCATED) | [
"14",
"14"
] | null | 4 | "Let's step through the reasoning trace to count how many times the model verifies an intermediate c(...TRUNCATED) | ["22 divided by (14 - 6), that's 22 divided by 8, which is 2.75.","14 divided by (22 - 6) is 14/16, (...TRUNCATED) | null | 5 | "To answer your question—how many times does the model verify its higher-level reasoning (i.e., de(...TRUNCATED) | ["Hmm, the target is 14, and one of the numbers is already 14. Maybe I can use that somehow. But I h(...TRUNCATED) | null |
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