
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]


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On April 23rd, World Book Day, a certain school decided to purchase two types of books, "Education of Love" and "Elegance of Words," to create a literary campus atmosphere promoting reading. Through investigation, it was found that purchasing 2 copies of "Education of Love" and 3 copies of "Elegance of Words" costs a total of 126 yuan, while purchasing 3 copies of "Education of Love" and 2 copies of "Elegance of Words" costs a total of 109 yuan.  
$(1)$ Find the prices of one copy of "Education of Love" and "Elegance of Words" respectively.  
$(2)$ If the school plans to purchase a total of 200 books, with the quantity of "Education of Love" not exceeding 3 times the quantity of "Elegance of Words" and not less than 70 copies. Find the minimum total cost for the school to purchase the books.

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