
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 diameter 6 inches starts at point A and rolls along a customized track. The track consists of 3 subsequent arcs with radii $R_1 = 150$ inches, $R_2 = 200$ inches, and $R_3 = 120$ inches. The ball rolls on the inside for the second arc and on the outside for the first and third arcs. Calculate the distance the center of the ball travels from A to B.

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