
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 certain type of hovercraft has a maximum speed of 48 nautical miles per hour. The fuel cost per hour is directly proportional to the square of the speed. When the speed is 30 nautical miles per hour, the fuel cost per hour is 600 yuan. Other costs (regardless of the speed) are 864 yuan per hour. The distance between points A and B is 100 nautical miles, and the hovercraft travels from A to B at a constant speed.

1. Express the total cost y of traveling from A to B as a function of the speed x (nautical miles per hour), and specify the domain of the function.
2. At what speed (nautical miles per hour) is the total cost of traveling from A to B the smallest? What is the smallest total cost?

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