
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
$\text{EFGH}$ is a rectangle with $\text{H}$ as the center of a circle and $\text{G}$ on the circle. If $\text{EH}=5$ and $\text{GH}=12$, compute the area of the shaded region which is half of the circular area to the right of the rectangle $\text{EFGH}$.
A) $\frac{151\pi}{2} - 50$
B) $\frac{169\pi}{2} - 60$
C) $\frac{180\pi}{2} - 70$
D) $\frac{169\pi}{2} - 55$

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