
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
There are 9 people in a club. Every day, three of them went to a cafe together, while the others did not go to the cafe. After 360 days, it turned out that any two people in the club had been to the cafe together the same number of times. What is that number?

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