
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) of a product is related to the production volume x (in units) by the function y = 3000 + 20x - 0.1x^2 (where 0 < x < 240). If the selling price per unit is 25 ten thousand yuan, determine the minimum production volume required for the producer to break even (revenue not less than total cost).

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