
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 \(P\) and radius 4 inches is tangent at point \(D\) to a circle with center \(Q\), as illustrated. If point \(Q\) is on the smaller circle, determine the area of the shaded region between the two circles. Express your answer in terms of \(\pi\).

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