
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 manufacturer with experience in production and sales has established the following statistical relationship for production and sales: The total cost of producing x (in hundreds of units) is G(x) (in ten thousand yuan), with a fixed cost of 2.8 ten thousand yuan, and a variable cost of 1 ten thousand yuan per hundred units (total cost = fixed cost + variable cost). The sales revenue R(x) (in ten thousand yuan) follows the formula 
$$
R(x)= 
\begin{cases} 
-0.4x^{2}+4.2x & (0≤x≤5) \\ 
11 & (x＞5)
\end{cases}
$$
Assuming the product sells as much as it's produced (meaning production is in balance with sales), please solve the following:
(1) Determine the expression for the profit function y=f(x) (profit = sales revenue - total cost);
(2) Determine the range of production quantity x for the factory to be profitable;
(3) How many units should the factory produce to maximize profit?

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