
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
There is a 100km waterway from tourist attraction A to B, and a ferry company has launched a cruise sightseeing project. It is known that the hourly fuel cost of the cruise ship is directly proportional to the cube of the speed, and other costs amount to 3240 yuan per hour. The maximum speed of the cruise ship is 50km/h. When the cruise ship's speed is 10km/h, the fuel cost is 60 yuan per hour. Assuming the cruise speed is $v$ km/h, the total cost for a one-way trip of the cruise ship from A to B is $S$ yuan.

(1) Express the total cost $S$ for a one-way trip of the cruise ship from A to B as a function $S=f(v)$ of the cruise speed $v$.

(2) When is the total cost $S$ for a one-way trip of the cruise ship from A to B the least, and what is the cruise speed $v$ at that point? Also, calculate the minimum total cost.

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