
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 concentric circles have radii of 6 inches and 3 inches respectively. Both circles are tangent at point P. Two bugs begin a journey from point P simultaneously, one crawling along the larger circle at \(4\pi\) inches per minute, and the other crawling along the smaller circle at \(3\pi\) inches per minute. Calculate the number of minutes before they next meet at point P.

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