
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 7 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, one along the larger circle at $4\pi$ inches per minute, the other along the smaller circle at $3\pi$ inches per minute. How many minutes will it take before their next meeting at point P, and how far will each bug have traveled by then?

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