
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
Given that bus types $A$, $B$, and $C$ all depart at 6:00 AM from a certain station, with departure intervals of 10 minutes, 12 minutes, and 15 minutes, respectively, if Xiaoming arrives at the station at some time between 8:00 AM and 12:00 PM to catch one of these buses, what is Xiaoming's average waiting time in minutes?

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