
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
A circular pond has a diameter of 16 feet and is crossed by a straight wooden bridge 4 feet wide, one edge of which passes through the center of the pond. Calculate the area of the pond that remains uncovered by the bridge.
A) $\frac{128\pi}{3} + 64\sqrt{3}$
B) $\frac{128\pi}{3} + 32\sqrt{3}$
C) $64\pi - 32\sqrt{3}$
D) $96\pi$
E) $64\pi - 16\sqrt{3}$

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