
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
The "Qinmi No. 9" golden passion fruit from Guangxi is deeply loved by customers for its "sweet and strong fragrance." A supermarket purchased a batch of golden passion fruit for $3600 and quickly sold out. The supermarket then purchased a second batch of golden passion fruit for $5400. At this point, a large amount of fruit was on the market, and the weight purchased was twice that of the first batch. However, the price per kilogram of the golden passion fruit in the second batch was $5 cheaper than the first batch.

$(1)$ What is the unit price per kilogram for the first and second batches of golden passion fruit purchased by the supermarket?

$(2)$ If both batches of golden passion fruit are sold at the same price, in order to ensure that the profit margin after selling all the golden passion fruit is not less than $50\%$ (excluding other factors), what should be the minimum selling price per kilogram set by the supermarket for the golden passion fruit?

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