
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
Consider the following scenario: a smaller circle with a radius of 3 feet is placed on the left side of a rectangular region and a larger circle with a radius of 5 feet is positioned on the right side, but they are separate and do not overlap. The rectangular region extends 2 feet above and below each circle’s center, and enough width is present to accommodate each circle with 1 foot of space on either side in the width. Calculate the total area of the shaded regions (areas not occupied by the circles but enclosed within the rectangle).

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