
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 locations A and B is $1000km$. A truck travels from A to B at a constant speed, which must not exceed $80km/h$. It is known that the hourly transportation cost (unit: Yuan) consists of variable costs and fixed costs. The variable cost is $\frac{1}{4}$ of the square of the speed, and the fixed cost is $a$ Yuan;  
(I) Express the total transportation cost $y$ (Yuan) as a function of speed $v(km/h)$, and specify the domain of this function;  
(II) If $a=400$, to minimize the total transportation cost, at what speed should the truck travel?

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