
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 Shanghai-Hangzhou Expressway is 166 kilometers long. Suppose a car enters the expressway from Xinzhuang Town, Shanghai, and travels to Hangzhou at a constant speed of no less than 60 kilometers per hour and no more than 120 kilometers per hour. The hourly transportation cost $y$ (in yuan) of the car consists of a variable part and a fixed part: the variable part is directly proportional to the square of the speed $v$ (kilometers per hour) with a proportionality constant of 0.02; the fixed part is 200 yuan.
(1) Express the total transportation cost $y$ (in yuan) as a function of speed $v$ (kilometers per hour), and specify the domain of this function;
(2) At what speed should the car travel to minimize the total transportation cost? What is the minimum transportation cost in yuan?

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