
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 relationship between the total cost $y$ (in ten thousand yuan) and the output $x$ (in units) of a product is given by the function $y = 3000 + 20x - 0.1x^2$, where $x \in (0, 240)$. Given that the selling price per unit is 25 ten thousand yuan, find the minimum output $x$ such that the producer does not incur a loss (sales revenue is not less than the total cost).

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