
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 company's annual fixed cost for producing a certain brand of clothing is ¥100,000. An additional ¥27,000 is required to produce every 1,000 pieces. Suppose the company produces and sells $x$ thousand pieces of this brand of clothing within a year, with the sales revenue per thousand pieces being $R(x)$ thousand yuan defined by
$$
R(x) =
\begin{cases}
10.8 - \frac{1}{30}x^2 & (0 < x \leq 10) \\
\frac{108}{x} - \frac{1000}{3x^2} & (x > 10)
\end{cases}
$$
(1) Write down the expression for the annual profit $W$ (in thousand yuan) as a function of the annual production quantity $x$ (in thousand pieces).  
(2) At what production quantity (in thousand pieces) does the company achieve the maximum profit for this brand of clothing? (Note: Annual profit = Annual sales revenue - Annual total cost)

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