
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 ship's fuel cost per hour, $P$ (in yuan), as a function of its speed $v$ (in kilometers per hour), is given by $P=k{v}^{3}$. It is known that when the speed is 10 kilometers per hour, the fuel cost is 5 yuan per hour, and the other costs unrelated to speed are 80 yuan per hour.

(1) Express the fuel cost per hour, $P$ (in yuan), as a function of speed $v$ (in kilometers per hour);

(2) Given that the distance between two places, A and B, is 100 kilometers, what speed should the ship travel at to minimize the total cost of traveling from A to B?

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