
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 factory produces a type of product. It is known that the relationship between the production quantity \(x\) (in tons) and the price per ton \(P\) (in yuan/ton) of the product is defined by \(P = 24200 - \frac{1}{5}x^2\). Additionally, the cost to produce \(x\) tons is \(R = 50000 + 200x\) yuan. How many tons should the factory produce each month to maximize profit? What is the maximum profit? (Profit = Revenue - Cost)

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