
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 with two overlapping circles, the smaller circle has a radius of three feet, and the larger circle has a radius of five feet, overlapping such that the center of each circle lies on the circumference of the other. Calculate the total area outside the circles but within a rectangle that touches the furthest points of both circles. Assume all measurements are in feet.

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