
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 machinery manufacturing company has a total cost of $G(x)$ million yuan for producing $x$ hundred units of a product, where $x$ is the number of hundreds. The fixed cost is 2.8 million yuan, and the production cost for each hundred units is 1 million yuan (Total cost = Fixed cost + Production cost). The sales revenue $R(x)$ million yuan satisfies $R(x) = \begin{cases} -0.4x^2 + 4.2x & (0 \leq x \leq 5) \\ 11 & (x > 5) \end{cases}$. Assuming that all produced products can be sold, complete the following tasks:

(I) Write the profit function $y = f(x)$ analytic expression (Profit = Sales revenue - Total cost);

(II) How many units should the factory produce to maximize profit?

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