
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 factory produces a certain product. The relationship between the monthly production volume $x$ (in tons) and the price per ton $p$ (in yuan/ton) is given by the formula: $p=24200-\frac{1}{5}{{x}^{2}}$. The cost of producing $x$ tons is $R=50000+200x$ (in yuan). What is the monthly production volume that maximizes profit? What is the maximum profit? (Note: Profit = Revenue - Cost)

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