
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
In response to the requirements of garbage classification, to create a clean and tidy learning environment and to establish a harmonious and civilized campus environment, the affiliated high school of the university is preparing to purchase two types of classified garbage bins, $A$ and $B$. Through market research, it is found that the unit price of each set of type $A$ garbage bin is $150$ yuan less than the unit price of each set of type $B$ garbage bin. It is also known that the number of sets of type $A$ garbage bins that can be purchased with $18000$ yuan is twice the number of sets of type $B$ garbage bins that can be purchased with $13500$ yuan.<br/>$(1)$ Find the unit price of each set of type $A$ and type $B$ garbage bins, respectively;<br/>$(2)$ The school plans to purchase a total of $20$ sets of type $A$ and type $B$ garbage bins with no more than $8000$ yuan. How many sets of type $B$ garbage bins can be purchased at most?

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