
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
There are 25 gremlins, 20 imps, and 10 sprites at the Horizon Fantasy Meetup. The imps continue to avoid shaking hands among themselves. However, the sprites only shake hands with each other and with the gremlins, but not with the imps. Each pair of creatures shakes hands only once. How many handshakes occurred at this event?

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