
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
On April 23rd, it is "World Book Day," and two bookstores, A and B, held book purchase promotions on this day.  
Bookstore A: All books are sold at 20% off the list price;  
Bookstore B: For a total purchase price not exceeding $100, the books are charged at the original price. For the part exceeding $100, a 40% discount is applied.  
Let $x$ (in dollars) represent the total list price, and $y$ (in dollars) represent the amount to be paid.  
$(1)$ When $x > 100$, find the expression of the function $y$ in terms of $x$;  
$(2)$ Lele went to buy books on "World Book Day." When the total list price of the books he wants to buy is more than $100, which bookstore should he choose to pay less?

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