
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 distance between places A and B is 400 kilometers. A car travels from A to B at a constant speed, and the speed must not exceed 100 km/h. It's known that the transportation cost per hour $t$ (in yuan) as a function of the speed $x$ (in km/h) is given by $t= \frac{1}{19200}x^4 - \frac{1}{160}x^3 + 15x$.
(1) What is the total transportation cost when the car travels at a constant speed of 60 km/h?
(2) To minimize the total transportation cost, what should be the car's speed, and what is the minimum cost?

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