
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 are participating in a school sports-entertainment game. They only have one pair of roller skates between the two of them, and need to traverse a distance of 3 km as quickly as possible. They start simultaneously, with one running and the other roller-skating. At any moment, the one on roller skates can leave them for the other and continue running without them. This exchange can occur as many times as desired. Find the minimum time for both friends to complete the distance (which is determined by who finishes last), given that Vasya's running and roller skating speeds are 4 km/h and 8 km/h respectively, while Petya's speeds are 5 km/h and 10 km/h. Assume that no time is lost during the exchange of roller skates.

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