
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 reduce inventory quickly, the mall decides to take appropriate price reduction measures. After investigation, it was found that for each item that is reduced by 1 yuan, the mall can sell 2 more items on average per day.

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

$(2)$ Let the price reduction per item be $x$ yuan. Then the daily sales volume of the mall will increase by ______ items per item, and the profit per item will be ______ yuan (expressed in algebraic expression containing $x$).

$(3)$ Under the normal sales conditions mentioned above, how much should the price of each item be reduced by for the mall to achieve a daily profit of 2000 yuan?

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