
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 math interest group in a school has 14 students. They form \( n \) different project teams. Each project team consists of 6 students, each student participates in at least 2 project teams, and any two project teams have at most 2 students in common. Find the maximum value of \( n \).

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