
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
The Absent-Minded Scientist commutes to work on weekdays using the Ring Line of the Moscow Metro from "Taganskaya" station to "Kievskaya" station, and back in the evening. When he enters the station, he boards the first arriving train. It is known that in both directions, trains run at approximately equal intervals. The train traveling via the northern route (through "Belorusskaya") takes 17 minutes to go from "Kievskaya" to "Taganskaya" or vice versa, while the train traveling via the southern route (through "Paveletskaya") takes 11 minutes.

According to his long-term observations, the train traveling counterclockwise arrives at "Kievskaya" on average 1 minute and 15 seconds after the clockwise train arrives. The same is true for "Taganskaya." Moreover, the scientist notes that his average travel time from home to work is 1 minute less than his average travel time from work to home. Find the expected interval between trains traveling in one direction.

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