
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 fruit market sells a high-end fruit. The original price is $50$ yuan per kilogram. After two consecutive price reductions, the price becomes $32$ yuan per kilogram. It is known that the percentage of reduction is the same each time.  
$(1)$ Find the percentage of reduction each time.  
$(2)$ If there is a profit of $10$ yuan per kilogram, and the market can sell $500$ kilograms per day. After a market survey, the market decides to increase the price by $1$ yuan per kilogram. This will result in a decrease in daily sales by $20$ kilograms. The market now needs to ensure a daily profit of $6000$ yuan and reduce inventory as soon as possible. How much should the price increase per kilogram to meet these requirements?

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