
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 certain product with a fixed cost of $20,000. The cost increases by $100 for each unit produced. Given that the total revenue $R$ is related to the annual production volume $x$ as follows: $R=R(x)=\begin{cases} 400x-\frac{1}{2}x^2, & (0\leqslant x\leqslant 400) \\ 80,000, & (x > 400)\end{cases}$, determine the annual production volume that maximizes the total profit.

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