
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
At a gathering, there are 25 gremlins and 20 imps. Owing to some conflicts, only 10 imps are willing to shake hands with the gremlins, and each of these imps shakes hands with just 15 of the gremlins. All gremlins are in good terms with each other and shake hands amongst themselves as well. Calculate the total number of handshakes at this assembly.

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