
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 conclusion of a match, each of the six members of a basketball team shakes hands with each of the six members of the opposite team, and all of the players shake hands with three referees. How many handshakes occur?

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