
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]


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A shopping mall purchases a batch of goods from a manufacturer at a price of $20 per item. If the retail price of the product is $p$, the sales volume $Q$ (in units) and the retail price $p$ (in units of yuan) have the following relationship: $Q=8300-170p-p^2$. Determine the retail price that maximizes profit.

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