
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 have radii of 7 inches and 3 inches, respectively, and are tangent at point P. Two bugs start crawling from point P; however, the bug on the smaller circle starts 2 minutes later. The first bug crawls along the larger circle at $4\pi$ inches per minute, and the second bug along the smaller circle at $3\pi$ inches per minute. How many minutes after the first bug starts moving will they meet again at point P?

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