
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
There is a circular subway line that operates with both an inner and outer ring, each being 30 kilometers long (ignoring the difference in length between the two).  
(1) When 9 trains are operating simultaneously on the inner ring, in order to ensure the maximum waiting time for passengers on the inner ring is 10 minutes, find the minimum average speed required for the inner ring trains;  
(2) Under a new adjusted plan, it requires that the inner ring trains have an average speed of 25 kilometers per hour and the outer ring trains have an average speed of 30 kilometers per hour. There are a total of 18 trains operating on both the inner and outer rings. To ensure that the difference in maximum waiting time between passengers on the inner and outer rings does not exceed 1 minute, how many trains should be operated on each ring?

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