
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 mall purchases a batch of goods from a manufacturer at 20 yuan per item. If the retail price of the goods is set at P yuan, then the sales volume Q (unit: pieces) and the retail price P (unit: yuan) have the following relationship: $Q=8300-170P-P^2$. What should the retail price be set at to maximize the gross profit (gross profit = sales revenue - purchase cost)?

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