
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 stationery store stipulates that if one purchases 250 or more exercise books at a time (including 250 books), they can pay at the wholesale price; if one purchases fewer than 250 books, they must pay at the retail price. Li, a teacher, went to the store to buy exercise books for the 8th-grade students. If he buys 1 book for each 8th-grade student, he must pay $240$ yuan at the retail price; if he buys 60 more books, he can pay at the wholesale price and will need to pay $260$ yuan.  
$(1)$ Find the range of the number of 8th-grade students in the school.  
$(2)$ If the amount needed to buy 288 books at the wholesale price is the same as the amount needed to buy 240 books at the retail price, find the number of 8th-grade students in the school.

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