
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
In the diagram, the smaller circles each touch the larger circle internally and also each other externally. The radius of the larger circle is $10$. Determine the area of the shaded region if the smaller circles are congruent.

[asy]
size(150);
import graph;
filldraw(Circle((0,0),5),mediumgray);
filldraw(Circle((-2.5,2.165),1.5),white);
filldraw(Circle((-2.5,-2.165),1.5),white);
[/asy]

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