
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 time \\(u\\) is directly proportional to the cube of its speed \\(v\\). If the speed of the ship is \\(20km/h\\), the fuel cost is \\(40\\) yuan per hour, and the other costs are \\(270\\) yuan per hour, which do not change with speed.  
\\((1)\\) Find the function relationship between \\(u\\) and \\(v\\);  
\\((2)\\) Find the speed of the ship at which the cost per kilometer of sailing is the lowest (the maximum speed of the ship is \\(bkm/h\\)).

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