
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 from the point C to D along a track composed of four semicircular arcs. The radii of the arcs are $R_1 = 120$ inches, $R_2 = 50$ inches, $R_3 = 90$ inches, and $R_4 = 75$ inches, respectively. Calculate the distance that the center of the ball travels from C to D.
A) $108\pi$ inches
B) $212\pi$ inches
C) $258\pi$ inches
D) $335\pi$ inches
E) $400\pi$ inches

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