
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
Before the Dragon Boat Festival, a supermarket plans to purchase two types of fruits, A and B, to meet people's shopping needs. It is understood that the purchase price and selling price of fruits A and B are as shown in the table below:

| Fruit Price | A   | B   |
|-------------|-----|-----|
| Purchase Price (yuan/kg) | $16$ | $20$ |
| Selling Price (yuan/kg) | $20$ | $25$ |

If the supermarket purchases a total of $200$ kilograms of these two fruits, with the weight of fruit A not less than three times the weight of fruit B, how should the supermarket purchase in order to obtain the maximum profit, and what is the maximum profit?

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