
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
Four cyclists. Four identical circles represent four tracks. The four cyclists start from the center at noon. Each moves along their track at speeds: the first at 6 km/h, the second at 9 km/h, the third at 12 km/h, and the fourth at 15 km/h. They agreed to ride until they all meet again in the center for the fourth time. The length of each circular track is $\frac{1}{3}$ km.

When will they meet again?

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