
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
Six couples are at a gathering. Each person shakes hands exactly once with everyone else except their own spouse and except one person who is not their spouse. How many handshakes are exchanged?

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