
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
A competition consists of \( n \) true/false questions. After analyzing the responses of 8 participants, it was found that for any two questions, exactly two participants answered "True, True"; exactly two participants answered "False, False"; exactly two participants answered "True, False"; and exactly two participants answered "False, True". Determine the maximum value of \( n \).

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