
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 $AB=CD=4$ and $BC=DA=8$. The rectangle undergoes a 90° clockwise rotation about point $D$, then another 90° clockwise rotation about the new position of point $C$ after the first rotation. What is the total length of the path traveled by point $A$?
A) $6\pi$
B) $2\sqrt{5}\pi$
C) $4\pi$
D) $(4 + 2\sqrt{5})\pi$

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