
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 bus station has exactly one passenger bus arriving each day between $8:00 \sim 9:00$ and one between $9:00 \sim 10:00$, with the arrival times being random and mutually independent.

Given that a passenger arrives at the station at $8:20$, find the expected waiting time for the passenger (accurate to the minute).

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