
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
The Zhangzhou City Museum wants to protect a precious artifact by filling a transparent and sealed rectangular glass protective cover with a protective liquid. The total cost that the museum needs to pay consists of two parts: ① The volume of this liquid inside the cover is 0.5 cubic meters less than the capacity of the protective cover, and the cost of each cubic meter of liquid is 500 yuan; ② A certain amount of insurance fee needs to be paid, and the insurance fee paid is inversely proportional to the capacity of the protective cover. When the capacity is 2 cubic meters, the insurance fee paid is 4000 yuan.
(I) Find the functional relationship between the total cost y that the museum needs to pay and the capacity x of the protective cover.
(II) Find the minimum value of the total cost that the museum needs to pay.

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