
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 \(C\) to a circle with center \(B\). Assume that point \(B\) is located on the smaller circle. What is the area of the shaded region formed by these circles? Express your answer in terms of \(\pi\).

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