
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
After a gymnastics meet, each gymnast shook hands once with every gymnast from every other team but not with their own teammates. Afterwards, two coaches, each from a different team, came down and shook hands with each gymnast from their respective teams. There were a total of 325 handshakes. What is the fewest number of handshakes that one of the coaches could have participated in?

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