
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 women's doubles tennis tournament, there were four teams of two women. After the tournament, each woman shook hands once with each of the other players except her partner, except one player who did not shake hands with anyone from one specific team. What is the number of handshakes that occurred?

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