
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
The excellent traditional Chinese culture is the "root" and "soul" of the Chinese nation, which is the cultural root and gene that must be passed down from generation to generation. In order to inherit the excellent traditional culture, a certain school purchased several sets of "Romance of the Three Kingdoms" and "Water Margin" comic books for each class. The price of each set of "Romance of the Three Kingdoms" comic books is $60 more expensive than the price of each set of "Water Margin" comic books. It is known that the school spent $3600 on "Romance of the Three Kingdoms" comic books and $4800 on "Water Margin" comic books. The number of sets of "Romance of the Three Kingdoms" comic books purchased is half the number of sets of "Water Margin" comic books purchased. Find the price of each set of "Water Margin" comic books.

$(1)$ Let the price of each set of "Water Margin" comic books be $x$ dollars. Express the following using expressions containing $x$:
The price of each set of "Romance of the Three Kingdoms" comic books is ______ dollars, the number of sets of "Romance of the Three Kingdoms" comic books purchased is ______, and the number of sets of "Water Margin" comic books purchased is ______.

$(2)$ Write down the equations and complete the solution to this problem.

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