
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 point A to point B along a track made of four semicircular arcs. The radii of these arcs are $R_1 = 120$ inches, $R_2 = 40$ inches, $R_3 = 70$ inches, and $R_4 = 50$ inches. The first and third arcs are such that the ball is on the outside, and the second and fourth arcs place the ball on the inside of the track. Determine the total distance the center of the ball travels.
A) $250\pi$ inches
B) $270\pi$ inches
C) $280\pi$ inches
D) $300\pi$ inches
E) $320\pi$ inches

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