
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
The diagonals of the inscribed quadrilateral \(ABCD\) intersect at point \(P\), where the angle \(APB\) is obtuse. Points \(E\) and \(F\) are the midpoints of sides \(AD\) and \(BC\), respectively. From point \(E\), a perpendicular is drawn to line \(AC\), and from point \(F\), a perpendicular is drawn to line \(BD\). These perpendiculars intersect at point \(Q\). Find the angle between lines \(PQ\) and \(CD\).

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