
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
The total cost y (in ten-thousand yuan) and the production quantity x (in units) of a product are related by the function y = 3000 + 20x - 0.1x^2, where x ∈ (0, 240). If the selling price per unit is 250,000 yuan, calculate the minimum production quantity required to avoid a loss.

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