
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
Cyclists Petya, Vlad, and Timur simultaneously started a warm-up race on a circular bike path. Their speeds are 27 km/h, 30 km/h, and 32 km/h, respectively. After what minimum time will they find themselves at the same point on the track again? (The length of the bike path is 400 meters.)

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