
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 factory plans to sell a product. The salespeople do not determine the price of this product based on the production cost but through a survey on how much stock retailers would order at different prices. The survey established the relationship $P = -750x + 15000$, where $P$ is the quantity of goods retailers order (in units), and $x$ is the price per unit paid by the retailers (in yuan). It is estimated that the material and labor production cost per unit of this product is 4 yuan, and the total fixed cost of producing this product in the factory is 7000 yuan (fixed costs are other expenses besides materials and labor). To maximize profit, how much should the factory charge retailers per unit? And what is the maximum profit at this time?

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