
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
Diagonals of a quadrilateral  $ABCD$  are equal and meet at point  $O$ . The perpendicular bisectors to segments  $AB$  and  $CD$  meet at point  $P$ , and the perpendicular bisectors to  $BC$  and  $AD$  meet at point  $Q$ . Find angle  $\angle POQ$ .

by A.Zaslavsky

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