
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
In recent years, there have been continuous trade frictions between China and the United States. Especially, the restrictions imposed by the United States on Huawei, a Chinese company. Despite the strong blockade and pressure from the United States to resist Huawei's 5G technology, Huawei has not backed down. In 2018, Huawei not only set a record for net profit but also showed strong growth overseas. This year, a certain enterprise of Huawei in China plans to further increase its market competitiveness by producing a new smartphone using new technology in 2020. Through market analysis, it is known that to produce this new smartphone for the whole year, a fixed cost of $2.5$ million needs to be invested. For each production of $x$ (in thousand units) of the smartphone, an additional cost of $R(x)$ million needs to be invested, where $R(x)=\begin{cases}10x^2+100x, & 0<x<40\\ 701x+\frac{10000}{x}-9450, & x\geqslant 40\end{cases}$. According to market research, the selling price of each smartphone is $0.7$ million, and all the smartphones produced within the year can be sold.

(1) Find the function relationship $W(x)$ (in million yuan) of the profit in 2020 with respect to the annual production quantity $x$ (in thousand units) (Profit = Revenue - Cost);

(2) When the production quantity in 2020 is how many thousand units, will the enterprise make the maximum profit? What is the maximum profit?

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