
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
A highway, where buses run continuously, crosses a railroad. Every hour, there are two trains that reach the highway, precisely at $n$ hours and at $n$ hours and 38 minutes, where $n$ takes all values from 0 to 23. Each time a train passes, a gate blocking the highway is lowered for 5 minutes. It is required to schedule buses such that they run at regular intervals of $T$ minutes and none of the buses are delayed at the crossing. For which intervals between buses, less than half an hour, is it possible to schedule their movement in this way?

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