
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
The region in question is called the crescent moon falcata, which is bound by the following: a portion of the circle with radius 4 centered at (0,0) in the second quadrant, a portion of the circle with radius 2 centered at (0,2) in the second quadrant, and the line segment from (0,0) to (-4,0). Determine the area of the crescent moon falcata.
A) $4\pi$
B) $6\pi$
C) $8\pi$
D) $10\pi$
E) $12\pi$

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