
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
Green Jianchang, we build together. Our school actively responds to the county's call for garbage classification. We purchased two types of garbage bins, $A$ and $B$, from a certain shopping mall for recyclable and non-recyclable garbage. It is known that the $B$ brand garbage bin is $30$ yuan more expensive than the $A$ brand garbage bin. The amount spent on purchasing $A$ brand garbage bins is the same as twice the amount spent on purchasing $B$ brand garbage bins with $2400$ yuan and $1500$ yuan, respectively.  
$(1)$ Find out how much it costs to buy one $A$ brand garbage bin and one $B$ brand garbage bin.  
$(2)$ If our school decides to purchase a total of $30$ garbage bins of types $A$ and $B for no more than $4000$ yuan, how many $B$ brand garbage bins can our school purchase at most?

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