
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 ecological demonstration garden actively responds to the government's economic policy of "practicing ecological organic concepts and promoting the development of organic agriculture," cultivating excellent varieties and planting a variety of organic fruits. A supermarket purchased Fruit A for $300 and Fruit B for $300 for the first time from the demonstration garden. The cost of Fruit B is 1.5 times the cost of Fruit A, and the supermarket purchased 10kg more of Fruit A than Fruit B.  
$(1)$ Find the cost per kilogram of Fruit A and Fruit B, respectively.  
$(2)$ The fruits purchased for the first time were quickly sold out. To meet consumer demand, the supermarket is preparing to purchase Fruit A and Fruit B totaling 100kg, with the quantity of Fruit A being at least 3 times that of Fruit B. If the selling price of Fruit A is $13 per kilogram and the selling price of Fruit B is $20 per kilogram, how many kilograms of each type of organic fruit should the supermarket purchase to maximize profit for the second time, and what is the maximum profit?

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