
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 touch the larger circle internally at the larger circle's diameter and also touch each other at one point. The radius of the larger circle is increased to $10.$ Each smaller circle has a radius, which is half of the larger circle's radius. What is the area of the shaded region?

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