
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 eighteen imps are at the Annual Mischief Convention. Due to a recent squabble, five specific gremlins refuse to shake hands with each other or with any other gremlins. However, these five gremlins will shake hands with all imps. The remaining gremlins and all of the imps shake hands with each other as before: imps do not shake hands with each other but will shake hands with any gremlin. How many handshakes occur at the convention?

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