
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 in a shopping mall sells an average of 30 items per day, with a profit of 50 yuan per item. In order to have a major promotion in the year 618, the mall decides to take appropriate price reduction measures. After investigation, it was found that for every 1 yuan reduction in price per item, the mall can sell 2 more items per day.

$(1)$ If the price of the product is reduced by 3 yuan per item on a certain day, how much profit can be made on that day?

$(2)$ In order to reduce inventory and ensure a daily profit of 2000 yuan, how much should the price of each item be reduced by?

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