
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
Two circles, one with a radius of 6 inches and the other with a radius of 3 inches, are tangent at point P. Two bugs start crawling at the same time from point P, the first along the larger circle at $4\pi$ inches per minute, and the second along the smaller circle at $3\pi$ inches per minute. Determine how many minutes elapse before they next meet at point P.

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