
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
Thirty gremlins and twenty imps are at the Annual Mischief Convention. Due to recent disagreements, ten of these gremlins refuse to shake hands with each other, but they still shake hands with the remaining gremlins and all the imps. The imps, maintaining their usual stance, refuse to shake hands among themselves but will shake hands with all gremlins. Calculate the total number of handshakes at the convention.

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