
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 school plans to purchase two types of bookshelves, A and B, to place the newly purchased books. It is known that the cost price of each type A bookshelf is $20\%$ higher than that of each type B bookshelf. The number of type A bookshelves purchased for $5400$ yuan is $6$ less than the number of type B bookshelves purchased for $6300$ yuan.

1. What is the cost price of each type A bookshelf?
2. If the school plans to purchase a total of $60$ bookshelves of these two types, with the number of type B bookshelves not exceeding twice the number of type A bookshelves, how should the school make the purchase to minimize the cost of purchasing the bookshelves?

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