
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 center of a circle is \( O \), with a diameter \( AB \). Let \( P \) be an interior point of the circle. Chords \( AQ \) and \( BR \) connect \( P \) to \( A \) and \( B \), respectively, with other endpoints \( Q \) and \( R \). The radius \( OQ \) intersects the chord \( BR \) at \( X \), and the radius \( OR \) intersects the chord \( AQ \) at \( Y \). What is the locus of points \( P \) for which the quadrilateral \( OXPY \) is a cyclic quadrilateral?

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