
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 dealer uses a type J truck to transport a certain type of fruit from an orchard to a fruit wholesale market that is 400 km away (fully loaded). According to calculations, when the type J truck is fully loaded, the fuel consumption per 100 km, μ (unit: L), and the speed, v (unit: km/h), have an approximate relationship of μ = $\begin{cases} \frac{100}{v} + 23, & 0 < v \leqslant 50 \\ \frac{v^2}{500} + 20, & v > 50 \end{cases}$. Apart from fuel costs, other costs such as labor wages and vehicle depreciation average 300 yuan per hour. The fuel price is 7.5 yuan per liter (L).
(1) Express the cost of transporting this truckload of fruit, y (yuan) (excluding return trip costs), as a function of speed, v.
(2) What speed should the truck maintain to minimize the cost of transporting this truckload of fruit?

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