
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 new construction, two circles overlap. The smaller circle has a radius of three feet and the larger circle has a radius of six feet. The circles intersect such that the distance between the centers equals the radius of the smaller circle. Calculate the total area of the unique shaded regions when both circles are drawn inside a rectangular region with one side equal to three times the diameter of the smaller circle and another side equal to four times the diameter of the larger circle.

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