
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
There are two circles ($C_{1}$ and $C_{2}$). Draw a secant line $QR$ through one of their intersection points, $P$, such that the central angles corresponding to the chords $QP$ and $PR$ are equal to each other.

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