
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
When a ship sails, the fuel cost per unit of time $u$ is directly proportional to the cube of its speed $v$, i.e., $u \propto v^3$. If the speed of the ship is 10 km/h, the fuel cost is 35 yuan per hour, and the other costs amount to 560 yuan per hour, which do not vary with speed. Given that the maximum speed of the ship is 25 km/h, find the speed of the ship in km/h at which the cost per kilometer of sailing is minimized.

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