
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 company has 15 buses in its parking lot, starting to dispatch buses at 6:00 AM (the first bus departs at exactly 6:00 AM), and then dispatches another bus every 6 minutes. Three minutes after the first bus departs, a bus enters the parking lot, and thereafter, a bus enters the parking lot every 8 minutes. The buses that enter the parking lot will be dispatched after the original 15 buses. The questions are:  
(1) At what time will there be no buses in the parking lot for the first time?  
(2) At what time will the bus company no longer be able to dispatch buses at 6-minute intervals on time? And calculate the minimum delay time for the first bus that cannot be dispatched on time.  
(3) If the bus company wants to ensure that buses can be dispatched at equal intervals from 6:00 AM to 8:00 PM, with other conditions unchanged, what is the minimum interval between dispatches (accurate to 1 minute)?  
(4) If the bus company plans to add some buses so that buses can be dispatched at 6-minute intervals from 6:00 AM to 8:00 PM, with other conditions unchanged, how many buses need to be added at least?

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