
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 community supermarket purchased two types of goods, A and B, for $6000. The number of items of type B is 15 more than half the number of items of type A. The cost and selling price of goods A and B are shown in the table below: (Note: Profit = Selling Price - Cost)

|           | A   | B   |
|-----------|-----|-----|
| Cost ($)  | 22  | 30  |
| Price ($) | 29  | 40  |

$(1)$ How many items of goods A and B did the supermarket purchase?  
$(2)$ If the supermarket sells all the goods A and B purchased, how much profit will it make?

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