
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 cargo ship travels at a constant speed between two points, A and B, which are 300 nautical miles apart, transporting goods. The transportation cost consists of fuel expenses and other expenses. It is known that the ship's hourly fuel cost is directly proportional to the square of its speed (with a proportionality constant of 0.5), and the other expenses amount to 800 yuan per hour. Additionally, the ship's maximum speed is 50 nautical miles per hour.

(1) Please express the transportation cost $y$ (in yuan) from point A to point B as a function of the speed $x$ (in nautical miles per hour);

(2) To minimize the transportation cost from point A to point B, at what speed should the cargo ship travel?

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