
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
In the Tangwangchuan of Tianshui, Anning's peaches, and Tangwangchuan's Da Jie apricots are treasures. Tangwangchuan in Dongxiang Autonomous County, Linxia Prefecture, is a famous "home of peaches and apricots". The Da Jie apricots produced there are one of the three famous apricots in Gansu. They are loved by consumers for their large fruit size, sweet taste, and pleasant flavor. A supermarket purchased a batch of "Tangwangchuan Da Jie apricot slices" at a cost of $50$ yuan per kilogram. A survey found that when the selling price is $80$ yuan per kilogram, an average of $30$ kilograms can be sold per day. However, when the selling price decreases by $1$ yuan, an additional $2$ kilograms can be sold per day.<br/>$(1)$ Let $x$ represent the price reduction per kilogram. Express the actual selling price and sales quantity using an algebraic expression with $x$;<br/>$(2)$ If the supermarket wants the daily sales profit of this "Tangwangchuan Da Jie apricot slices" to reach $1000$ yuan, and to benefit the customers, how much should the price be reduced per kilogram?

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