
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
The chess clubs of Moscow, Saint Petersburg, and Kazan agreed to hold a tournament. Each Muscovite played exactly with 9 participants from Saint Petersburg and with \( p \) participants from Kazan. Each participant from Saint Petersburg played exactly with 6 participants from Moscow and with 2 participants from Kazan. Each participant from Kazan played exactly with 8 participants from Moscow and with 6 participants from Saint Petersburg. What is \( n \)?

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