
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. For each additional instrument produced, an additional ¥100 is invested. The total revenue function is given by $H(x)= \begin{cases} 400x-x^2, & (0 \leqslant x \leqslant 200) \\ 40000, & (x > 200) \end{cases}$, where $x$ is the monthly production volume of instruments. Profit is defined as total revenue minus total cost.
(I) Express profit as a function of the monthly production volume $x$;
(II) For what value of monthly production volume $x$ does the workshop achieve maximum profit? What is the maximum profit in yuan?

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