
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
Given a ball with a diameter of 6 inches, where the first and second arcs of a track have radii of $R_1 = 150$ inches and $R_2 = 90$ inches, respectively, and the ball travels along the track via a straight segment of length 100 inches, calculate the distance the center of the ball travels from point A to B.

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