
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 fifteen imps are at the Annual Mischief Convention. Due to a spell, each imp shakes hands with only half of the gremlins. All gremlins are friendly and shake hands with each other as well as with any imp that approaches them. Each pair of creatures shakes hands at most once. How many handshakes occur at this convention?

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