
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 English club is attended by 20 gentlemen. Some of them are acquaintances (the acquaintances are mutual, i.e., if A knows B, then B knows A). It is known that there are no three gentlemen in the club who are all mutually acquainted with each other.

One day, the gentlemen came to the club, and each pair of acquaintances shook hands (once). What is the maximum number of handshakes that could have been made?

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