
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 protective gas. The total cost the museum needs to pay 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 of the gas is 1,000 yuan per cubic meter; ② A certain insurance fee needs to be paid, and the insurance fee is inversely proportional to the volume of the protective cover. When the volume is 2 cubic meters, the insurance fee is 8,000 yuan.  
(1) Find the function relationship between the total cost $y$ the museum needs to pay and the volume $V$ of the protective cover;  
(2) Find the minimum total cost the museum needs to pay;  
(3) If the protective cover is required to be in the shape of a right rectangular prism with a height of 2 meters, and the total cost the museum needs to pay does not exceed 9,500 yuan, find the maximum base area of the protective cover.

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