
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 shopping mall purchases a batch of goods at a price of $220$ yuan per item. When the selling price of each item is $280$ yuan, they can sell 30 items per day. In order to expand sales for the "$618" shopping festival, the mall decides to promote sales by appropriately reducing prices. After investigation, it was found that if the price of each item is reduced by $1$ yuan, the mall can sell 3 more items per day. Let $x$ represent the price reduction per item.

$(1)$ The daily sales volume of the mall increases by ______ items, and the profit per item is ______ yuan (expressed as an algebraic expression involving $x$);  
$(2)$ To make the profit from selling this kind of item reach $3600$ yuan per day, and to reduce inventory more effectively, how much should the price of each item be reduced by?

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