
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 department in a shopping mall sells a brand of shirts. On average, they can sell 30 shirts per day, with a profit of $40$ yuan per shirt. In order to increase sales and reduce inventory, the mall decides to reduce the price. After investigation, it was found that for every $1$ yuan reduction in price, they can sell an additional $2$ shirts per day.  
$(1)$ If the price is reduced by $3$ yuan, the average daily sales quantity will be ______ shirts;  
$(2)$ By how much should the price be reduced per item so that the store makes a daily sales profit of $1200$ yuan?

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