
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 composed of three sections: two semicircular arcs and one straight segment. The radii of the semicircular arcs are $R_1 = 120$ inches and $R_3 = 90$ inches, respectively. Between these arcs, there is a straight segment of 50 inches in length. The ball always remains in contact with the track and does not slip. Calculate the distance that the center of the ball travels from A to B.

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