
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
Natural  $n \geq 2$  is given. Group of people calls  $n-compact$ , if for any men from group, we can found  $n$  people (without he), each two of there are familiar. 
Find maximum  $N$  such that for any  $n-compact$  group, consisting  $N$  people contains subgroup from  $n+1$  people, each of two of there are familiar.

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