
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 shopping mall sells goods at a price of $50$ yuan each, which were purchased at a unit price of $40$ yuan. When sold at this price, $500$ units can be sold. It is known that for this type of goods, for every increase of one yuan in the selling price, the sales volume decreases by $10$ units. To maximize profit, what should be the selling price per unit? What is the maximum profit?

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