
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 RMB per unit. If it's sold at a retail price of 50 RMB per unit, it can sell 50 units. It is observed that for each 1 RMB increase in retail price above 50 RMB, there is a decrease of 1 unit in sales volume. What should be the retail price to maximize the profit when selling this batch of goods? What is the maximum profit?

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