
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
Points $P, Q$, and $R$ are on a circle of radius $2r$, with $PQ = PR$ and $PQ > 2r$. The length of the minor arc $QR$ is $\pi r$. Calculate the ratio $\frac{PQ}{QR}$ if angles are measured in radians.
A) $\frac{2}{\pi}$
B) $\frac{2\sqrt{2}}{\pi}$
C) $2\sqrt{2}$
D) $2\pi$

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