
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 club has 99 members. Find the smallest positive integer $n$ such that if the number of acquaintances of each person is greater than $n$, there must exist 4 people who all know each other mutually (here it is assumed that if $A$ knows $B$, then $B$ also knows $A$).

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