
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
A rectangle with dimensions $2 \times 3$ is inscribed in a semicircle with the $3$-unit side lying along the diameter. The rectangle also touches a smaller circle placed exactly at the center of the semicircle's diameter. Calculate the area of the semicircle.
A) $\frac{25\pi}{12}$
B) $\frac{10\pi}{3}$
C) $\frac{25\pi}{8}$
D) $\frac{15\pi}{4}$

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