
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 ball with a diameter of 6 inches rolls along a path consisting of three semicircular arcs from point A to B. The radii of the arcs are $R_1 = 120$ inches, $R_2 = 50$ inches, and $R_3 = 100$ inches, respectively. Determine the distance the center of the ball travels along this path from A to B.
A) $250\pi$ inches
B) $267\pi$ inches
C) $280\pi$ inches
D) $300\pi$ inches

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