
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
In the first quadrant, there is a region known as the comet's tail region, surrounded by the quarter-circle of radius 6 with center (0,0), a quarter square with side 6, and a smaller quarter-circle of radius 2 centered at (0,2). The vertexes of the quarter square align with the quadrant axes. Determine the area of the comet's tail region.

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