
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 $500$ km. A truck travels from Xuzhou to Suzhou at a constant speed, with a maximum allowed speed of $100$ km/h. The transportation cost per hour of the truck (in yuan) consists of a variable part and a fixed part: the variable part is directly proportional to the square of the speed $v$(km/h), with a proportionality coefficient of $0.01$; the fixed part is $100$ yuan.
  1. Express the total transportation cost $y$(yuan) as a function of the speed $v$(km/h), and state 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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