
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 of radius 7 inches and the other of radius 3 inches, are tangent at point P. Two bugs start crawling at the same time from point P, one crawling along the larger circle at \(4\pi\) inches per minute, the other crawling along the smaller circle at \(3\pi\) inches per minute. How many minutes will it take for them to meet again at point P?

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