
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  $24$  participants attended a meeting. Each two of them shook hands once or not. A total of  $216$  handshakes occured in the meeting. For any two participants who have shaken hands, at most  $10$  among the rest  $22$  participants have shaken hands with exactly one of these two persons. Define a *friend circle* to be a group of  $3$  participants in which each person has shaken hands with the other two. Find the minimum possible value of friend circles.

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