
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
Peter arrived at the bus stop of a school bus that makes equidistant stops along its route. Not seeing the bus on the road, he decided to run and catch the bus at one of the next stops. Peter runs in such a way that at any moment he can notice the appearance of the bus behind him. Upon seeing the bus, Peter can either turn back or continue in the same direction. It is known that the bus travels at a speed 3 times that of Peter's running speed, and that he can see the bus from a distance of no more than 0.8 km. Find the maximum distance between the bus stops such that regardless of whether Peter turns back when he sees the bus or not, he will be able to catch the bus at a stop. (Ignore the time the bus spends at the stop.)

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