
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 shopping mall purchased two types of goods, A and B, from the manufacturer. The cost price of each unit of type A is $20 more than the cost price of each unit of type B. The cost of purchasing 5 units of type A is the same as the cost of purchasing 6 units of type B.<br/>$(1)$ Find the cost price of each unit of type A and type B.<br/>$(2)$ The shopping mall purchased a total of 80 units of type A and type B from the manufacturer for $9000. After increasing the cost price of type A by 50% and offering an 20% discount on the selling price, and selling type B with a profit of $30 per unit, how much profit will the shopping mall make after selling all units of type A and type B?

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