
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
The fixed cost of producing a certain instrument in a workshop is ¥10,000, and each additional unit produced increases the cost by ¥100. The total revenue is given by the function: $H(x)=\begin{cases} 400x-x^{2}, & (0\leqslant x\leqslant 200), \\ 40000, & (x > 200) \end{cases}$, where $x$ is the monthly production volume (Total Revenue = Total Cost + Profit).

(Ⅰ) Express the profit (denoted as $f(x)$) as a function of the monthly production volume $x$;

(Ⅱ) At what monthly production volume is the profit maximized? What is the maximum profit?

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