
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
Quadrilateral $PQRS$ is inscribed in a circle with segment $PR$ a diameter of the circle. If $m\angle PQR = 45^\circ$ and $m\angle QPR = 60^\circ$, find the ratio of the area of $PQRS$ to the area of the circle. Express your answer as a common fraction in simplest radical form in terms of $\pi$ as $\frac{a+\sqrt{b}}{c\pi}$, where $a,$ $b,$ and $c$ are positive integers.

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