
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 $210$ yuan each. When the selling price of each item is $270$ yuan, they can sell 30 items per day. In order to prepare for the "Double Eleven 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.  
$(1)$ What is the profit of the mall from selling this item each day before the price reduction?  
$(2)$ In order to make the profit of selling this item each day at the mall reach twice the profit before the price reduction, 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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