
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
Given that the cost $C$ of a certain product is related to the output $q$ by the equation $C=50000+200q$, and the selling price $p$ of the product is related to the output $q$ by the equation $p=24200-\frac{1}{5}q^2$, find the value of $q$ at which the profit is maximized.

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