
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
In June and July each year, various summer fruits ripen successively, and it is also the peak season for fruit sales. A certain merchant seized the business opportunity and promoted the sales of two types of fruits, A and B, in June. It is known that the total sales amount of type A fruit in June is 12000 yuan, and the total sales amount of type B fruit is 9000 yuan. The selling price of type B fruit is 1.5 times that of type A fruit, and the sales quantity of type B fruit is 1000 kg less than that of type A fruit.

$(1)$ Find the selling price of type A fruit in June.

$(2)$ In July, the merchant plans to sell a total of 5000 kg of type A and type B fruits. To increase sales efforts, the selling price of type A fruit was reduced by 30% based on the price in June, and the selling price of type B fruit was discounted by 40% based on the price in June. To ensure that the total sales amount in July is not less than 23400 yuan, how many kilograms of type A fruit should the merchant sell at most?

$(3)$ Under the conditions of $(2)$, if the cost price of type A fruit is 2.7 yuan/kg and the cost price of type B fruit is 3.5 yuan/kg, how much profit can the merchant make in July?

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