
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, each circle is divided into two equal areas. $O$ is the center of the largest circle, which has an area of $144\pi$. A smaller circle has its center on the vertical diameter of the largest circle and is tangent internally to the largest circle. A third circle, which is half the size of the smaller circle, is concentric with the smaller circle. What is the total area of the shaded regions in all three circles?

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