
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
For a pharmaceutical manufacturing company, the relationship between production costs, sales revenue, and profit is an important issue. Research on such a company has shown that its production costs $y$ (in ten thousand yuan) and sales revenue $z$ (in ten thousand yuan) are both functions of the production quantity $x$ (in tonnes), specifically: $y=x^3-24x^2+63x+10$, $z=18x$.
① Try to write the function that expresses the company's production profit $w$ (in ten thousand yuan) in terms of the quantity produced $x$.
② At what production quantity does the company achieve the maximum profit, and what is that maximum profit?

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