
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 certain product has a wholesale price of $40 per unit. If it is sold for $50 per unit, all 50 units can be sold. For each $1 increase in the selling price, one less unit can be sold. In order to achieve the maximum profit, what should be the optimal selling price of this product? Additionally, find the maximum profit.

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