
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 plans to purchase two different types of notebooks, type A and type B. It is known that the unit price of type A notebooks is $1 less than the unit price of type B notebooks, and the quantity of type A notebooks that can be purchased with $110 is the same as the quantity of type B notebooks that can be purchased with $120.  
$(1)$ Find the unit prices of type A and type B notebooks.  
$(2)$ The school plans to purchase a total of 100 notebooks of type A and type B, with the quantity of type B notebooks not exceeding 3 times the quantity of type A notebooks. What is the minimum cost for this purchase?

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