
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
An equilateral  $12$ -gon has side length  $10$  and interior angle measures that alternate between  $90^\circ$ ,  $90^\circ$ , and  $270^\circ$ . Compute the area of this  $12$ -gon.

*Proposed by Connor Gordon*

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