
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 supermarket sells a certain product, with an average daily sales of 20 items and a profit of 40 yuan per item. In order to increase sales volume and profit, the store has implemented a price reduction measure. After a period of time, it was found that for every 1 yuan reduction in unit price, an average of 2 more items are sold per day.  
$(1)$ If the price is reduced by 3 yuan, the average daily sales quantity will be ______ items;  
$(2)$ To reduce inventory quickly and ensure that the store's daily sales profit is 1200 yuan, how much should the price of each item be reduced by?

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