
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 a side length of \(1\). Points \(P\) and \(Q\) are located on segments \(AB\) and \(AD\) respectively. If the perimeter of \(\triangle APQ\) is \(2\), find \(\angle PCQ\).

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