
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
Each twin shook hands with $5\cdot 3=15$ triplets and with each of the other $7$ twins except his or her sibling. The number of handshakes that involved a twin is given by the sum $15\cdot 16+7\cdot 15$, as each of these $8$ twins shook hands with $15$ triplets and each of these $7$ twins shook hands with the other $7$ twins.

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