
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 match, each of the five members of a basketball team shakes hands with each of the five members of the opposing team. In addition, each player shakes hands with three referees after the game. How many handshakes occur in total?

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