
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
At a certain station, there is exactly one passenger train arriving between 8:00-9:00 and 9:00-10:00 each day, but the arrival times are random and independent. The arrival time distribution is given by the following table:

| Arrival Time | 8:10 / 9:10 | 8:30 / 9:30 | 8:50 / 9:50 |
|--------------|--------------|-------------|-------------|
| Probability  | 1/6          | 1/2         | 1/3         |

A passenger arrives at the station at 8:20. What is the expected waiting time for the next train? (Round your answer to the nearest minute.)

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