
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 23, 2023, which is the 28th World Book Day, a school organized a themed event called "Make Reading a Habit, Let the Fragrance of Books Fill the Campus - Reading • Dream Soaring" to appreciate the happiness of reading, understand the essence of life, and share the joy of reading. For this event, the school ordered a batch of new books for each class. Class 1 of the first year ordered 4 sets of "Selected Works of Lao She" and 2 sets of "Four Great Classical Novels" for a total cost of 480 yuan. Class 2 of the first year ordered 2 sets of "Selected Works of Lao She" and 3 sets of "Four Great Classical Novels" for a total cost of 520 yuan. <br/>$(1)$ Find the cost of each set of "Selected Works of Lao She" and "Four Great Classical Novels". <br/>$(2)$ The school is preparing to purchase a total of 20 sets of "Selected Works of Lao She" and "Four Great Classical Novels" for a total cost not exceeding 1720 yuan. The number of sets of "Selected Works of Lao She" purchased should not exceed twice the number of sets of "Four Great Classical Novels". How many purchasing plans does the school have? Please design them.

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