
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 cost price of a certain product is 40 yuan per item. When the selling price is set at 60 yuan per item, 300 items can be sold per week. Now, it is necessary to reduce the price, and according to market research: for every 1 yuan reduction in price, 20 more items can be sold each week. Under the premise of ensuring profit, solve the following questions:  
(1) If the price is reduced by x yuan per item and the weekly profit from selling the goods is y yuan, please write the function relationship between y and x, and find the range of values for the independent variable x;  
(2) If the minimum unit of price reduction is 1 yuan, how much should the price be reduced to maximize the weekly profit? What is the maximum profit?

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