
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 $A, B,$ and $C$ each have a radius of 2. Circles $A$ and $B$ are tangent to each other at one point. Circle $C$ has a point of tangency with the midpoint of $\overline{AB}.$ What is the area inside circle $C$ but outside circles $A$ and $B$?
A) $4\pi$  
B) $2\pi$  
C) $2\pi + 2$  
D) $2\pi + 4$  
E) $4\pi + 4$

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