
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 attend the Annual Mischief Convention. Due to some alliances, exactly five imps are willing to shake hands with each other but refuse to shake hands with the remaining imps. All imps shake hands with all gremlins. Meanwhile, being sociable, all gremlins shake hands with each other as well as all the imps. Calculate the total number of handshakes at the convention.

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