
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
In the city of Omsk, a metro line was built in a straight line. On this same line is the house where Nikita and Yegor live. Every morning, they simultaneously leave the house for their lessons, after which Yegor runs to the nearest metro station at a speed of 12 km/h, while Nikita walks along the metro line to another station at a speed of 6 km/h. Despite this, Nikita always manages to reach his lesson on time, whereas Yegor does not, even though he doesn't delay anywhere. Find the maximum possible speed of the metro trains, given that it is constant and an integer. (Assume the school is located directly at a certain metro station, distinct from the given ones).

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