
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
The 19th National Congress pointed out that China's electric vehicle revolution has already begun. By replacing gasoline/diesel cars with new energy vehicles, China is implementing a plan that will reshape the global automotive industry. In 2018, a company plans to import new energy vehicle production equipment. Through market analysis, the fixed cost for the whole year is 25 million yuan, and for each production of $x$ (hundred cars), an additional cost of $C(x)$ million yuan is required, where $C(x)=\begin{cases} 10x^{2}+100x,0 < x < 40 \\ 501x+\frac{10000}{x}-4500,x\geqslant 40 \end{cases}$. According to market research, each car is priced at 50,000 yuan, and all cars produced within the year can be sold out that year.

(1) Find the profit function $L(x)$ (in million yuan) in terms of the annual production quantity $x$ (in hundred cars) for the year 2018. (Profit = Sales revenue - Cost)

(2) In 2018, how many hundred cars should be produced to maximize the company's profit? And find the maximum profit.

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