
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 gremlins, twenty imps, and ten sprites are attending the Fantasy Creatures Gala. The imps only shake hands with gremlins and sprites. Gremlins are affable and shake hands with their fellow gremlins as well as the imps. Sprites, the shyest of all, only shake hands with imps. Calculate the total number of handshakes at the gala.

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