
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 has a fixed cost of 20,000 yuan for producing a type of electronic instrument. The cost increases by 100 yuan for each instrument produced. The total revenue function is given by \(R(x)= \begin{cases} 400x- \frac {1}{2}x^{2}, & 0\leqslant x\leqslant 400 \\ 80000, & x > 400\end{cases}\), where \(x\) is the production volume (unit: units);  
(1) Express the profit \(f(x)\) as a function of the production volume \(x\) (profit = total revenue - total cost);  
(2) At what production volume \(x\) does the company achieve maximum profit? What is the maximum profit in yuan?

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