
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 workshop produces a type of instrument with a fixed cost of $7500. Each additional unit of the instrument requires an additional investment of $100. The total revenue function is given by: $H(x) = \begin{cases} 400x - x^2, (0 \leq x \leq 200) \\ 40000, (x > 200) \end{cases}$, where $x$ is the monthly production volume of the instrument. (Note: Profit = Total Revenue - Total Cost)
(I) Express the profit as a function of the monthly production volume $x$;
(II) What monthly production volume will yield the maximum profit for the workshop? What is the maximum profit?

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