
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 store 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: items) is related to the retail price $p$ (unit: yuan) by the following relationship: $Q = 8300 - 170p - p^2$. How much should the goods be priced at to maximize the gross profit $L$, and what is the maximum gross profit?

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