
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 Shouning, "Golden Silk Button" is a local specialty product that is highly favored by consumers. A certain supermarket purchased a batch of "Golden Silk Button" at a cost of $24$ yuan per kilogram. A survey found that when the selling price is $40$ yuan per kilogram, an average of $20$ kilograms can be sold per day. Furthermore, when the selling price is reduced by $1$ yuan, an additional $2$ kilograms can be sold per day.  
$(1)$ Let $x$ represent the price reduction per kilogram. Express the actual selling price and sales quantity using an algebraic expression involving $x$.  
$(2)$ If the supermarket wants the daily sales profit of this "Golden Silk Button" to reach $330$ yuan and provide benefits to customers, how much should the price be reduced per kilogram?

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