
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 B along a path made up of three semicircular arcs. The original radii of these arcs are $R_1 = 120$ inches, $R_2 = 50$ inches, and $R_3 = 70$ inches. Determine the total distance traveled by the center of the ball.

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