
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 certain middle school plans to purchase two types of bookshelves, type A and type B, to place the newly purchased books in order to create a literary campus. A survey found that if they buy 3 type A bookshelves and 2 type B bookshelves, it will cost a total of 1020 yuan; if they buy 4 type A bookshelves and 3 type B bookshelves, it will cost a total of 1440 yuan.  
$(1)$ What is the price of each type of bookshelf in yuan?  
$(2)$ If the school plans to purchase a total of 20 bookshelves of these two types, with the number of type B bookshelves not less than the number of type A bookshelves, and the school can provide a maximum of 4320 yuan, please design several purchasing plans for the school to choose from.

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