
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 certain military-industrial enterprise produces a type of precision electronic instrument with a fixed cost of $20,000. For each additional instrument produced, an additional $100 is invested. The total revenue is given by the following function: $R(x) = \begin{cases} 400x - \frac{1}{2}x^2, & 0 \leq x \leq 400 \\ 80,000, & x > 400 \end{cases}$, where $x$ is the monthly production volume.
(1) Represent the profit as a function of the monthly production volume;
(2) For what value of the monthly production volume does the company obtain the maximum profit? What is the maximum profit in dollars? (Note: Total Revenue = Total Cost + Profit.)

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