
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 weekdays, the Absent-Minded Scientist travels to work on the ring line of the Moscow Metro from "Taganskaya" station to "Kievskaya" station in the morning and back in the evening (see the diagram).

Upon entering a station, the Scientist boards the first arriving train. It is known that trains travel in both directions at approximately equal intervals. The travel time from "Kievskaya" to "Taganskaya" or back is 17 minutes via the northern route (through "Belorusskaya"), and 11 minutes via the southern route (through "Paveletskaya"). As per his long-standing habit, the Scientist always makes calculations. One day, he calculated that based on many years of observations:

- The train going counterclockwise arrives at "Kievskaya" on average 1 minute and 15 seconds after the train going clockwise arrives at "Kievskaya". The same is true for "Taganskaya".
- The Scientist takes on average 1 minute less time traveling from home to work than from work to home.

Find the mathematical expectation of the interval between trains traveling in one direction.

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