
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
Given that circles $A$ and $B$ each have a radius of 1 and are tangent to each other, and circle $C$ with a radius of 2 touches the point where circles $A$ and $B$ are tangent, calculate the area inside circle $C$ but outside circles $A$ and $B$.

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