
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 single book purchase with a total list price not exceeding $100, the price is calculated at the original price. For the part exceeding $100, a 40% discount is applied.  
$(1)$ Let $x$ (unit: yuan) represent the total list price, and $y$ (unit: yuan) represent the amount to be paid. Find the analytical expressions of the functions $y$ in terms of $x$ for the two bookstores' discount methods.  
$(2)$ On "World Book Day," which bookstore is more cost-effective to purchase books from?

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