
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
A company produces a product with a fixed cost of $20,000. Each unit of the product increases the cost by $100. The relationship between the total revenue $R$ and the annual production volume $x$ is given by $R(x) = \begin{cases} -\frac{x^{3}}{900} + 400x, & 0 \leqslant x \leqslant 390 \\ 90,090, & x > 390 \end{cases}$. Determine the number of product units produced annually when the total profit is maximized.

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