
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 a diagram, $AB$ and $CD$ are diameters of a circle with radius 6, intersecting perpendicularly at the center $O$. Additionally, there’s a shaded region created by two smaller diameters, $EF$ and $GH$, of a concentric circle with radius 3, also intersecting at $O$ at right angles. What is the area of the shaded region created by the intersection of the regions inside each smaller circle but outside the larger circle?

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