
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
Point \( P \) lies inside a convex pentagon \( A F Q D C \) such that \( F P D Q \) is a parallelogram. Given that \(\angle F A Q = \angle P A C = 10^\circ\), and \(\angle P F A = \angle P D C = 15^\circ\). What is \(\angle A Q C\)?

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