
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
To protect a precious cultural relic, the museum needs to fill a colorless glass sealed protective cover with a protective gas. It is assumed that the total cost paid by the museum consists of two parts: ① The volume of the gas inside the cover is 0.5 cubic meters less than the volume of the protective cover, and the cost per cubic meter of gas is 1,000 yuan; ② A certain insurance fee needs to be paid, and the insurance fee paid is inversely proportional to the volume of the protective cover, when the volume is 2 cubic meters, the insurance fee paid is 8,000 yuan.  
(1) Find the function relationship between the total cost $y$ paid by the museum and the volume $V$ of the protective cover;  
(2) Find the minimum total cost paid by the museum.

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