
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 certain circular subway line operates with both inner and outer loops, each being 30km long (ignoring the difference in length between the inner and outer loops).
(1) When 9 trains are running on the inner loop at the same time, to ensure the longest waiting time for passengers on the inner loop is 10 minutes, find the minimum average speed of the trains on the inner loop;
(2) Under a new adjustment plan that requires the average speed of the trains on the inner loop to be 25km/h and that of the outer loop to be 30km/h. Now, with a total of 18 trains running on both the inner and outer loops, how many trains should be allocated to each loop to minimize the difference in the longest waiting times for passengers on both loops?

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