
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 unit time $u$ is directly proportional to the cube of its velocity $v$. If the ship's velocity is 10 km/h, the fuel cost is 35 yuan per hour. The other costs amount to 560 yuan per hour, which do not vary with velocity. What should be the ship's velocity so that the cost per kilometer is minimized?

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