
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 store purchases goods at a unit price of 40 yuan. When they sell the goods for 50 yuan each, they can sell 500 units. It is known that with each one yuan increase in price, the sales volume decreases by 10 units. To achieve maximum profit, what should the selling price be set at? What is the maximum profit?

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