
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 deals in a high-end fruit, originally priced at $50$ yuan per kilogram. 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 decided to take appropriate price increase measures, but stipulated that the price increase per kilogram cannot exceed $8$ yuan. If the price increases by $1$ yuan per kilogram, the daily sales volume will decrease by $20$ kilograms. <br/>$(1)$ After two consecutive price reductions, the price per kilogram is $32$ yuan. If the percentage of each decrease is the same, find the percentage of each decrease; <br/>$(2)$ Now, the market needs to ensure a daily profit of $6000$ yuan. How much should the price per kilogram increase by? <br/>$(3)$ The maximum profit for the fruit is ______ yuan (directly fill in the answer).

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