
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 goblins and twenty trolls are attending the Enchanted Creatures Gala. The trolls, having sworn an oath of silence, refuse to shake hands with each other but will shake hands with all of the goblins. The goblins, being very social, shake hands with each other and with all the trolls. Determine the total number of handshakes at the gala.

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