
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 a test with 15 true or false questions.  It is known that every 2 people have at least 1 correct answer in common.  What is the minimum number of people that could have correctly answered the question which the most people were correct on?

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