
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
Rectangle $ABCD$ lies in a plane with $AB = CD = 3$ and $BC = DA = 8$. This rectangle is rotated $90^\circ$ clockwise around $D$, followed by another $90^\circ$ clockwise rotation around the new position of point $C$ after the first rotation. What is the length of the path traveled by point $A$?
A) $\frac{\pi(8 + \sqrt{73})}{2}$
B) $\frac{\pi(8 + \sqrt{65})}{2}$
C) $8\pi$
D) $\frac{\pi(7 + \sqrt{73})}{2}$
E) $\frac{\pi(9 + \sqrt{73})}{2}$

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