
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
A factory has a batch of goods that need to be transported by sea from location A to location B. The maximum sailing speed of the ship is 60 nautical miles/hour. The distance between location A and location B is 600 nautical miles. The transportation cost per hour consists of fuel cost and other costs. The fuel cost per hour is proportional to the square of the ship's speed, with a proportionality constant of 0.5, and the other costs are 1250 yuan per hour.
(I) Express the total transportation cost y (in yuan) as a function of speed x (in nautical miles/hour).
(II) What speed should the ship maintain to minimize the total transportation cost?

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