
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
Consider a region with two circles where the larger circle has a radius three times the radius of the smaller circle. The diameter of the smaller circle is 3 units. The smaller circle is tangent to the larger circle from inside, at a point on the circumference of the larger circle. Find the area of the gray region which is enclosed within the larger circle but outside the smaller circle. Express your answer in terms of $\pi$.

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