
When tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.

[ASSESS]

[ADVANCE]

[VERIFY]

[SIMPLIFY]

[SYNTHESIZE]

[PIVOT]

[OUTPUT]

You should strictly follow the format below:

[ACTION NAME]

# Your action step 1

# Your action step 2

# Your action step 3

...

Next action: [NEXT ACTION NAME]


system
60 people participate in a brain teaser game. There are a total of 10 questions, each person answers each question once, and the total number of correct answers is 452. It is known that each person has answered at least 6 questions correctly. There are 21 people who answered exactly 6 questions correctly, 12 people who answered exactly 8 questions correctly, and an equal number of people who answered exactly 7 and exactly 9 questions correctly. How many people answered all 10 questions correctly?

Present the answer in LaTex format: \boxed{Your answer}
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