
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 stationery store that does wholesale and retail business stipulates that if you buy more than 300 pencils at a time (not including 300), you can pay at the wholesale price. If you buy 300 pencils or fewer (including 300), you can only pay at the retail price. Xiaoming went to the store to buy pencils. If he buys 1 pencil for each 8th-grade student, he can only pay at the retail price, which requires 120 yuan. If he buys 60 more pencils, he can pay at the wholesale price, and still needs 120 yuan.  
$(1)$ In what range is the total number of 8th-grade students in this school?  
$(2)$ If buying 360 pencils at the wholesale price costs the same as buying 300 pencils at the retail price, how many 8th-grade students are there in this school?

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