
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 original diagram, the larger circle (with center $O$) has an area of $100\pi$. A smaller circle, called Circle A, is inscribed in the larger circle such that its top edge is tangent to the diameter of the larger circle. Another smaller circle, called Circle B, touches the center of the larger circle and is half the diameter of Circle A. Assume each circle is divided into two equal areas, shaded and unshaded. Calculate the total area of only the shaded regions.

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