
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 mixed doubles badminton tournament, there were four teams. Two teams consist of two players each, and two teams consist of three players each. After the tournament, each player shook hands only once with each of the other players except their own teammates. How many handshakes occurred?

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