
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 Xuzhou and Suzhou is 500 kilometers. A truck travels from Xuzhou to Suzhou at a constant speed, with a regulated maximum speed of 100 kilometers per hour. The hourly transportation cost (in yuan) of the truck consists of a variable part and a fixed part: the variable part is directly proportional to the square of the speed $v$ (in kilometers per hour), with a proportionality constant of 0.01; the fixed part is 100 yuan.
(1) Express the total transportation cost $y$ (in yuan) as a function of the speed $v$ (in kilometers per hour) and identify the domain of this function.
(2) What speed should the truck travel at to minimize the total transportation cost?

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