
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 four feet is tangent at $D$ to a circle with center $Q$, as shown. If point $Q$ is on the smaller circle, what is the area of the shaded region? Express your answer in terms of $\pi$.

[asy]
filldraw(circle((0,0),8),gray,linewidth(2));
filldraw(circle(4dir(-30),4),white,linewidth(2));

dot((0,0));
dot(4dir(-30));
dot(8dir(-30));

label("$Q$",(0,0),NW);
label("$P$",4dir(-30),NE);
label("$D$",8dir(-30),SE);
[/asy]

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