
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]


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The relationship between the total cost $y$ (in ten thousand yuan) and the production quantity $x$ (in units) is given by the function $y=3000+20x-0.1x^2$, where $x\in(0,240)$. If the selling price per unit is 250,000 yuan, calculate the minimum production quantity for the producer to break even.

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