
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

Vasya and Petya, who are participating in a school sports-entertainment game, need to cover a distance of 3 km as quickly as possible, having only one pair of roller skates between the two of them. They start simultaneously, one running and the other running on roller skates. At any moment, the one on roller skates can leave them for the other to use and continue running without them. This exchange can be done as many times as necessary. Find the minimum time needed to cover the distance, determined by the last one to finish, if Vasya's running and skating speeds are 4 km/h and 8 km/h respectively, and Petya's are 5 km/h and 10 km/h. Assume no time is lost during the transitions.

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