
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 class is going to buy some table tennis balls and paddles. The situation is as follows: Store A and Store B sell the same brand of table tennis balls and paddles. The price of a pair of paddles is $48, and the price of a box of table tennis balls is $12. After negotiations, Store A gives a free box of table tennis balls for every pair of paddles purchased, while Store B offers a 10% discount on the total price. The class needs 5 pairs of paddles and $x$ boxes of table tennis balls (at least 5 boxes). Questions:<br/>$(1)$ Express the costs of purchasing from Store A and Store B using algebraic expressions;<br/>$(2)$ When 40 boxes of table tennis balls are needed, calculate and determine which store is more cost-effective to purchase from;<br/>$(3)$ When 40 boxes of table tennis balls are needed, can you provide a more cost-effective method? Please write down your purchasing method and the total cost.

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