
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
Twenty-five gremlins and twenty imps gather at the Annual Mischief Convention. The imps, due to their quarrelsome nature, refuse to shake hands with each other but are willing to shake hands with all of the gremlins. The gremlins, being very sociable creatures, shake hands with each other as well as with all of the imps. How many handshakes occur at this convention?

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