
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 circles $A, B,$ and $C$ each have a radius of 2, and circles $A$ and $B$ share one point of tangency, with circle $C$ intersecting circle $A$ at one of the endpoints of $\overline{AB}$ and also having a point of tangency with the midpoint of $\overline{AB}.$ Calculate the area inside circle $C$ but outside circle $A$ and circle $B.$

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