
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 library plans to purchase two types of books, A and B. It is known that the price of each book of type A is $2.5$ times the price of each book of type B. Buying type A books with $800$ yuan alone results in $24$ fewer books than buying type B books alone with $800$ yuan. What are the prices per book for type A and type B books?

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