
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
Through a point outside the parabola \( y^{2}=2px \ (p>0) \), two tangent lines \(PA\) and \(PB\) are drawn, with points of tangency \(A\) and \(B\) respectively. Let the circumcenter of triangle \(\triangle PAB\) be \(Q\), and suppose \(Q\) does not coincide with the focus \(F\) of the parabola. Find \(\angle PFQ\).

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