
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
Three circles are tangent at point P. The first circle has a radius of 7 inches, the second a radius of 3 inches, and a third circle, tangent to the first, has a radius of 4 inches. Three bugs start crawling at point P, one along each circle: the first at \(4\pi\) inches per minute, the second at \(3.5\pi\) inches per minute, and the third at \(2\pi\) inches per minute. How many minutes before the first two bugs next meet at point P?

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