
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 center $A$ and radius 4 inches is tangent at point $C$ to a circle with center $B$. The center $B$ is 5 inches away from the center $A$. If the radius of the larger circle is 9 inches, find the area of the shaded region that lies outside the smaller circle but inside the larger circle.

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