
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 ten pixies are attending a Fantasy Creatures Ball. The pixies, due to a spell, can only shake hands with an even number of goblins. Goblins are friendly and shake hands with each other as well as all the pixies. How many handshakes occur during the ball?

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