
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 has dimensions AB=CD=4 and BC=AD=8. The rectangle is rotated 90° clockwise about corner D, then rotated 90° clockwise about the corner C's new position after the first rotation. What is the length of the path traveled by point A?
A) $8\sqrt{5}\pi$  
B) $4\sqrt{5}\pi$  
C) $2\sqrt{2}\pi$  
D) $4\sqrt{2}\pi$

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