
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 cylinder with a diameter of 6 inches rolls from point A to point B along a path comprising three quarter-circle arcs with radii 150 inches, 90 inches, and 120 inches, respectively. The cylinder remains in contact with the path without slipping. Determine the distance traveled by the center of the cylinder.
A) $180\pi$
B) $181.5\pi$
C) $182\pi$
D) $183\pi$

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