
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
Given that the annual profit y (in ten thousand yuan) of a certain manufacturer is a function of the annual output x (in ten thousand units), as described by the function y = -\frac{1}{3}x^3 + 81x - 234, determine the annual output that will maximize the manufacturer's annual profit.

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