
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
The Wuhan Metro project is underway and will provide convenience for residents once it is operational. It is known that the time interval t (in minutes) between train departures on a certain line satisfies 10 ≤ t ≤ 30. Market research and calculations have shown that the number of passengers on the train is related to the time interval t. When 20 ≤ t ≤ 30, the train is fully loaded with 500 passengers. When 10 ≤ t < 20, the number of passengers decreases from the fully loaded state, and this decrease is proportional to the square of (20 - t). When the train departure time interval is 12 minutes, there are 244 passengers on the train. Denote the number of passengers on the train as P(t).

1. Find the expression for P(t) and determine the number of passengers when the train departure time interval is 18 minutes.
2. If the net revenue per minute for this line is given by Q(t) = $\frac{2p(t) + 400}{t}$ (in yuan), find the train departure time interval that maximizes the net revenue per minute and determine the maximum value.

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