
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 certain machinery manufacturer incurs a total cost $G(x)$ (in tens of thousands of yuan) for every $x$ (hundreds of units) produced, with a fixed cost of 2.8 tens of thousands of yuan and a variable cost of 1 tens of thousands of yuan per hundred units produced (total cost = fixed cost + variable cost). The sales revenue $R(x)$ (in tens of thousands of yuan) is given by
$$
R(x) = 
\begin{cases} 
-0.4x^2 + 4.2x & (0 \leq x \leq 5) \\
11             & (x > 5)
\end{cases}
$$
Assuming all produced units are sold, please solve the following problems:
(I) Write the expression for the profit function $y = f(x)$ (profit = sales revenue - total cost);
(II) How many units should the factory produce to maximize the profit?

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