
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
On a circular railway, there are \( n \) stations. At times, the station attendants communicate with each other via radio. At any given moment, the communication session is held by only two people. Over the course of a day, there was exactly one radio session between each pair of stations. For each station (considering only the sessions it engaged in), it turned out that it communicated with other stations alternately in the order of their arrangement on the railway (either clockwise or counterclockwise, with different directions for different stations), starting with one neighboring station and ending with the other. What could \( n \) be equal to?

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