
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 cities A and B are preparing to open a high-speed rail line with a total length of 1750km. It is known that the energy cost $W$ (in ten thousand yuan per hour) and the speed $V$ (in km/h) of the high-speed rail in operation are directly proportional to the cube of the speed. When the speed is 100km/h, the energy cost is 0.06 ten thousand yuan per hour, and the other costs (unrelated to speed) are 3.24 ten thousand yuan per hour. It is known that the maximum speed does not exceed $C$ (km/h) ($C$ is a constant, $0 < C \leq 400$).
(1) Find the function relationship between the total cost $y$ of the high-speed rail running the entire journey and the train speed $v$;
(2) At what speed of the high-speed rail will the total cost of running the entire journey be the lowest?

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