
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 school is preparing for the "Campus Reading Festival" and plans to purchase two types of books, A and B, as prizes. It is known that the unit price of type A books is $10 more than the unit price of type B books. Also, purchasing 3 type A books and 2 type B books costs a total of $130.  
$(1)$ What are the unit prices of type A and type B books?  
$(2)$ The school plans to purchase a total of 40 books of these two types, and the total budget does not exceed $980. How many type A books can be purchased at most?

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