
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 athletes started simultaneously from point \(A\) and ran in a straight line to point \(B\), each with their own constant speed. Upon reaching point \(B\), each of them instantly turned back and ran with another constant speed to the finish at point \(A\). Their coach ran alongside them and was always at a point where the sum of the distances to the athletes was minimized. It is known that the distance from \(A\) to \(B\) is 60 meters, and all athletes finished simultaneously. Could the coach have run less than 100 meters?

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