
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
At the end of a basketball tournament game, each of the seven members of the three participating teams shakes hands with each member of the other two teams, and all of the players shake hands with each of the three referees. How many handshakes occur?

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