
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
Circles \( A \) and \( B \) each have a radius of 1 and they touch each other at one point. Circle \( C \) has a radius of 2 and is tangential to the midpoint of the line segment \( \overline{AB} \) connecting the centers of circles \( A \) and \( B \). Determine the area contained within circle \( C \) but outside circles \( A \) and \( B \).
A) \( \pi + 2 \)
B) \( 3\pi + 4 \)
C) \( 2\pi + 3 \)
D) \( 4\pi + 3 \)

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