
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 during navigation is directly proportional to the cube of its speed. It is known that the fuel cost at a speed of 10 kilometers per hour is 6 yuan per hour, and other costs unrelated to speed are 96 yuan per hour. At what speed should the ship sail to minimize the total cost per kilometer traveled?

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