
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
Circle $A$ and Circle $B$ each have a radius of 1 and they touch each other. Circle $A$ is centered at $(0, 0)$ and Circle $B$ at $(2, 0)$. A larger Circle $C$ has a radius of 2 and touches Circle $B$ at $(3, 0)$. What is the area inside circle $C$ but outside Circle $A$ and Circle $B$?
A) \(2\pi\)
B) \(3\pi\)
C) \(4\pi\)
D) \( \frac{9\pi}{4} \)
E) \(6\pi\)

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