
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, there are two smaller circles within a larger circle. Both smaller circles are tangent to the larger circle and each other exactly at the center of the larger circle. The radius of the larger circle has been changed to $10.$ If each smaller circle has a radius that is one-third the radius of the larger circle, what is the area of the shaded region?

[asy]
size(120);
import graph;
filldraw(Circle((0,0),3),mediumgray);
filldraw(Circle((-1.5,0),1.5),white);
filldraw(Circle((1.5,0),1.5),white);
[/asy]

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