
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
Determine the selling price of a product that costs 8 yuan to purchase, such that when sold at 10 yuan, 100 units are sold daily. If the product's price is raised by 1 yuan, the daily sales volume decreases by 10 units. How should the selling price be set to maximize profit, and what is the maximum profit?

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