
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
Background:  
Supermarkets A and B both sell a certain brand of table tennis rackets and balls, with each racket priced at 50 yuan and each ball priced at 2 yuan. Currently, both supermarkets are having promotions, with Supermarket A offering a 10% discount on all goods, while Supermarket B offers 4 free balls with each racket purchased. Considering only the cost of purchasing rackets and balls,  
(1) If you only buy one racket and 10 balls from one supermarket, which supermarket is more cost-effective?  
Application:  
(2) A table tennis training center plans to buy n rackets of this brand, with each racket coming with k (k≥4) balls. If purchasing only from one supermarket, which supermarket is more cost-effective?  
Extension:  
(3) If the table tennis training center plans to buy n rackets of this brand, with each racket coming with 20 balls. Please calculate and design the most cost-effective purchasing plan.

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