
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
The school plans to purchase two types of books, Type A and Type B, as prizes for the "Campus Reading Festival". It is known that the unit price of Type A is 1.5 times that of Type B. If 600 yuan is spent to purchase only Type A books, there will be 10 fewer books than if the same amount was spent on Type B books.
(1) What are the unit prices of Type A and Type B books?
(2) If the school plans to purchase a total of 40 books of these two types and the budget does not exceed 1050 yuan, and it is required that the number of Type A books exceeds the number of Type B books, how many purchasing plans are possible?

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