
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 a gathering, there are eight individuals—four men and four women—of differing heights. Each man decides only to shake hands with individuals shorter than himself and doesn’t shake hands with any of the women. Each woman decides to shake hands only with women shorter than herself. How many handshakes take place if all participants follow these rules?

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