
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
Consider a newly designed region called a crescent moon falcata. It is bounded by the following:
- The portion of a circle of radius 4 centered at (0,0) that lies in the first quadrant.
- The portion of a circle with radius 1 centered at (0,2) that lies in the first quadrant.
- The line segment from (0,0) to (4,0).
Calculate the area of the crescent moon falcata.
A) $\frac{7\pi}{4}$
B) $\frac{9\pi}{4}$
C) $\frac{7\pi}{2}$
D) $6\pi$
E) $8\pi$

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