
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 side lengths $AB = CD = 3$ and $BC = DA = 8$. The rectangle undergoes three consecutive $90^\circ$ clockwise rotations: the first around point $D$, the second around the new position of point $C$ after the first rotation, and the third around the new position of point $B$ after the second rotation. Find the total length of the path traveled by point $A$.
A) $(4 + 2\sqrt{73})\pi$
B) $(4 + \sqrt{73})\pi$
C) $(3 + \sqrt{73})\pi$
D) $(5 + \sqrt{73})\pi$
E) $(4 + \sqrt{146})\pi$

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