
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
21 people take an exam with 15 true or false questions. It is known that there is at least one common correct answer between any two people. What is the minimum number of people who must answer correctly on the most correctly answered question? Explain the reasoning.

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