
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 rolling along a track consisting of 4 semicircular arcs with radii $R_1 = 150$ inches, $R_2 = 50$ inches, $R_3 = 90$ inches, and $R_4 = 120$ inches, find the distance the center of the ball travels over the course from A to B.

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