
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 $G(x)$ (in ten thousand dollars) for producing $x$ (in hundreds of units). The fixed cost is $2.8$ (ten thousand dollars), and the cost for producing each hundred units is $1$ (ten thousand dollars) $(G(x) = \text{Fixed Cost} + \text{Production Cost})$. The sales revenue $R(x)$ (in ten thousand dollars) satisfies $R(x) = \begin{cases} -0.4x^{2}+4.2x & (0\leqslant x\leqslant 5) \\ 11 & (x > 5)\end{cases}$, assuming that all produced units are sold, complete the following tasks:
(I) Write the analytical expression of the profit function $y=f(x)$ $(f(x) = \text{Revenue} - \text{Cost})$;
(II) How many units should the factory produce to maximize profits?

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