
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 "Internet $+$" has made our country's economy more dynamic. Live streaming sales is a vibrant sales method that utilizes the "Internet $+$" to sell local agricultural products from deep in the mountains to all parts of the country. Individual A assists in the sales of two local specialty products: peanuts and tea. It is known that the selling price of peanuts per kilogram is $40$ yuan lower than the selling price of tea per kilogram. The total selling price of selling $50$ kilograms of peanuts and $10$ kilograms of tea is the same.

$(1)$ Find the selling price per kilogram of peanuts and tea.

$(2)$ It is known that the cost of peanuts is $6$ yuan per kilogram and the cost of tea is $36$ yuan per kilogram. Individual A plans to assist in the sales of a total of $60$ kilograms of the two products, with a total cost not exceeding $1260$ yuan, and the quantity of peanuts sold not exceeding twice the quantity of tea sold. How many kilograms of peanuts and tea should be sold to obtain the maximum profit? What is the maximum profit?

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