
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 participate in an exam consisting of 15 true or false questions. It is known that for any pair of people, there is at least one question that both answered correctly. What is the minimum number of people who correctly answered the question that was answered correctly by the most people? Provide reasoning.

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