
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 Songjiang tram project is in full swing. After the tram starts operating, it will bring convenience to the public's travel. It is known that after the opening of a certain route, the tram interval $t$ (unit: minutes) satisfies $2 \leq t \leq 20$. According to market survey calculations, the tram’s passenger capacity is related to the departure interval $t$. When $10 \leq t \leq 20$, the tram is fully loaded with a capacity of 400 people. When $2 \leq t < 10$, the passenger capacity decreases, and the number of passengers reduced is directly proportional to the square of $(10-t)$, and when the interval is 2 minutes, the passenger capacity is 272 people. Let the tram's passenger capacity be $p(t)$.
(1) Find the expression for $p(t)$ and the passenger capacity when the departure interval is 6 minutes;
(2) If the net income per minute of the line is $Q = \dfrac{6p(t)-1500}{t} - 60$ (unit: yuan), what is the departure interval that maximizes the line’s net income per minute?

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