
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 4 inches and the other with a radius of 3 inches, are tangent at point P. A bug starts crawling from point P on the larger circle at 4π inches per minute, and another bug starts from an angle of 90 degrees on the smaller circle at 3π inches per minute. Calculate how many minutes it will be before their next meeting at point P.

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