
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
Huimin Fresh Supermarket sells a type of fruit with a cost price of $20$ yuan per kilogram. If it is sold at $40$ yuan per kilogram, they can sell $20$ kilograms per day. Market research shows that if the selling price of this fruit is reduced by $1$ yuan per kilogram, the daily sales volume will increase by $2$ kilograms.<br/>$(1)$ If the daily profit from selling this fruit remains the same, by how many yuan should the selling price per kilogram be reduced?<br/>$(2)$ By reducing the selling price, can the daily profit from selling this fruit reach $460$ yuan? If yes, by how many yuan should the selling price be reduced? If not, please explain why.

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