
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 three circles $A, B,$ and $C$ each with a radius of 1. A smaller circle $D$ with radius 0.5 is placed such that it is tangent to both circles $A$ and $B$. Circle $C$ is tangent to circle $D$. No other direct tangencies exist among $A, B,$ and $C$. Calculate the area inside circle $C$ but outside circles $A$, $B$, and $D$.
A) $\frac{3}{4}\pi$
B) $\frac{7}{8}\pi$
C) $\pi$
D) $\frac{5}{8}\pi$
E) $\frac{9}{8}\pi$

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