
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 product is currently priced at $60 per item, and 300 items can be sold each week. Market research indicates that if the price is adjusted, for every $1 decrease in price, an additional 30 items can be sold per week. It is known that the cost price of the product is $40 per item. Let the product's price decrease by $x$ dollars, and the profit per item be $y$ dollars per week.  
$(1)$ Express the following quantities in algebraic expressions involving $x$.  
① The profit per item is ______ dollars.  
② The number of items sold per week is ______ items.  
③ The functional relationship of $y$ with respect to $x$ is ______.  
$(2)$ How should the pricing be set to maximize the weekly profit, and what is the maximum value?

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