
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 tea specialty store in our city sells a certain brand of tea. The cost price is $240$ yuan per kilogram, and it is sold at $400$ yuan per kilogram. On average, $200$ kilograms are sold per week. After a market survey, it was found that if the unit price is reduced by $10$ yuan, the average weekly sales volume can increase by $40$ kilograms.  
$(1)$ If the store wants to make an average weekly profit of $41600$ yuan by selling this brand of tea, please answer:  
① By how much should the price per kilogram of tea be reduced?  
② If the store wants to maintain the same average weekly profit while offering the best discount to customers and winning the market, at what percentage of the original selling price should the tea be sold?  
$(2)$ Under the reduced price, can the store achieve an average weekly profit of $50000$ yuan by selling this brand of tea? Please explain the reason.

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