
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
In a gathering, there are 8 married couples. Each person shakes hands with everyone else except their own spouse and anyone wearing the same colored shirt as themselves. No person shares a shirt color with their spouse, and four unique shirt colors are represented equally by the attendees. How many handshakes occur?

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