
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
In a right triangle $PQR$ with $\angle PQR = 90^\circ$, a curved segment moves from point $P$ (with radius 0) to point $R$ (with radius 0) along an arc that is always perpendicular to line $QR$. The hypotenuse of triangle $PQR$ is 10 units. Determine the maximum area swept by the arc during its movement from $P$ to $R$.
A) \( \frac{15\pi}{2} \)
B) \( \frac{25\pi}{2} \)
C) \( 20\pi \)
D) \( 10\pi \)

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