
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 both inner and outer loops at the same time, with both loops being 35 kilometers long (ignoring the length difference between the loops).

(1) If 14 trains run on the inner loop at the same time, to ensure that the maximum waiting time for passengers on the inner loop does not exceed 6 minutes, what is the minimum average speed of the inner loop trains in kilometers per hour?

(2) The newly adjusted operational plan requires that the average speed of trains on the inner loop be 30 kilometers per hour and the average speed on the outer loop be 35 kilometers per hour. If there are 28 trains in total running on both loops, to ensure that the absolute difference in waiting times for passengers on the inner and outer loops does not exceed 0.5 minutes, how many trains should be operated on each loop?

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