
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, based on past experience, has discovered the following production and sales pattern: For every $x$ (in hundreds of units) produced, the total cost is $G(x)$ (in ten thousand yuan), where the fixed cost is 2.8 ten thousand yuan, and the production cost per hundred units is 1 ten thousand yuan (Total cost = Fixed cost + Production cost). The sales revenue $R(x)$ (in ten thousand yuan) satisfies:

\[R(x)=\begin{cases}
-0.4x^2+4.2x, & (0 \leq x \leq 5) \\
11, & (x > 5)
\end{cases}\]

Assuming that the product is sold as much as it is produced (i.e., production equals sales), based on the above pattern, solve the following problems:

(1) Write the expression for the profit function $y=f(x)$ (Profit = Sales Revenue - Total Cost);

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

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