
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 3 inches rolls from point A to point B along a track consisting of four arcs. The first two arcs are semicircular with radii $R_1 = 120$ inches and $R_2 = 50$ inches, respectively. The third arc is a quarter-circle with radius $R_3 = 75$ inches. Finally, there is a small semicircular arc with radius $R_4 = 20$ inches. Calculate the total distance the center of the ball travels.

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