
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
Two locations, A and B, are $s$ kilometers apart. A car travels from location A to location B at a constant speed, which does not exceed $60$ kilometers per hour. The hourly transportation cost $($in yuan$)$ consists of variable and fixed costs. The variable cost is directly proportional to the square of the speed $v($in kilometers per hour$)$. It is known that when the speed is $50$ kilometers per hour, the variable cost is $100$ yuan per hour. The fixed cost is $a$ yuan per hour.

1. Express the total transportation cost $y($in yuan$)$ as a function of the speed $v($in kilometers per hour$)$ and specify its domain.
2. At what speed should the car travel to minimize the total transportation cost?

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