
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
ABCDE is a regular pentagon. The star ACEBD has an area of 1. AC and BE meet at P, BD and CE meet at Q. Find the area of APQD.

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