
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
Square \(ABCD\) has side length 1, and points \(P\) and \(Q\) are located on sides \(AB\) and \(AD\) respectively. If the perimeter of \(\triangle APQ\) is 2, find the measure of \(\angle PCQ\) in degrees.

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