
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 store 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 and profits, the store implemented a price reduction measure. It was found that for each reduction of $1$ yuan in the selling price, the store could sell an additional 2 items per day, while ensuring that the profit per item is not less than $25$ yuan.<br/>$(1)$ If the price is reduced by $4$ yuan, the average daily sales quantity will be ______ items;<br/>$(2)$ By how much should the price of each item be reduced for the store to make a daily profit of $1050$ yuan?

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