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

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