
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 community plans to build two types of stalls, $A$ and $B$, to revitalize the "street vendor economy." The area occupied by each $A$ type stall is $2$ square meters more than the area occupied by each $B$ type stall. The cost of building each square meter of $A$ type stall is $40$ yuan, and the cost of building each square meter of $B$ type stall is $30$ yuan. Building stalls of type $A$ on $60$ square meters is exactly $\frac{3}{5}$ of the number of stalls of type $B$ that can be built on the same area.<br/>$(1)$ Find the area occupied by each $A$ and $B$ type stall in square meters.<br/>$(2)$ The community plans to build a total of $90$ stalls of types $A$ and $B$, with the number of $B$ type stalls being at least $3$ times the number of $A$ type stalls. Find the maximum cost to build these $90$ stalls.

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