
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
On April 23, 2023, which is the 28th "World Book Day," the Changfeng County Library held the "Enjoying Good Books in Changfeng with Reading" reading service activity. To meet the reading needs of the people in the county, the county library plans to purchase two types of books: social science books and children's books. According to the information obtained, 20 social science books and 40 children's books together cost 1600 yuan. It is known that the price of 20 social science books is 200 yuan more than 30 children's books (Note: the prices of the social science books purchased are the same, and the prices of the children's books purchased are the same). <br/>$(1)$ Find the price of each social science book and each children's book. <br/>$(2)$ If the county library requires the purchase of a total of at least 70 books, with 20 more children's books than social science books, and the total cost does not exceed 2000 yuan, please list all purchasing plans that meet the conditions.

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