
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 production cost $y$ (in ten thousand yuan) of a certain product is related to the production volume $x$ (in units) by the function $y = 0.1x^2 - 11x + 3000$. If the selling price per unit is 25 ten thousand yuan, calculate the production volume $x$ that the producer should set to achieve maximum profit.

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