
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
A circle of radius 3 is centered at $A$. An equilateral triangle with one vertex at $A$ has a side length of 6. Determine the difference between the area of the region that lies inside the circle but outside the triangle and the area of the region that lies inside the triangle but outside the circle.
A) $9\pi - 9$
B) $9(\pi - \sqrt{3})$
C) $3\pi - 3\sqrt{3}$
D) $18(\pi - \sqrt{3})$

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