
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 company operates a certain agricultural product. The profit from retailing one box of this agricultural product is $70, and the profit from wholesaling one box is $40.  
$(1)$ It is known that the company sold 100 boxes of this agricultural product in a certain month and made a total profit of $4600. What are the numbers of boxes of this agricultural product sold through retail and wholesale by the company in that month?  
$(2)$ According to the nature of the operation, the quantity of retail sales by the company cannot exceed 30% of the total quantity. Now, if the company wants to operate 1000 boxes of this agricultural product, how should they plan the quantities for retail and wholesale to maximize the total profit? What is the maximum total profit?

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