
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
Given the circle of radius $4$ centered at $(0,0)$ and the smaller quarter-circle of radius $2$ centered at $(2,0)$, and the line segment from $(0,0)$ to $(4,0)$, calculate the area of the eclipse falcata.

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