
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
Petya came to the bus stop, where the bus heads to school with equidistant stops, and decided to run to catch the bus at the next stops on the way to school since he didn't see the bus on the road. Petya runs in such a way that at any moment he could notice the bus appearing on the road behind him. Upon seeing the bus, Petya can either turn back or maintain his direction of movement. It is known that the bus travels at a speed 5 times greater than Petya's running speed, and he can notice the bus at a distance of no more than 0.6 km. Find the maximum possible distance between the stops so that, regardless of whether Petya turns back upon seeing the bus or not, he can catch the bus at a stop. (Do not consider the time the bus spends at a stop)

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