
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 (2018). In 2018, a certain company planned to introduce new energy vehicle production equipment. Through market analysis, the fixed cost to be invested throughout the year is 2500 million yuan. For each production of x (hundreds of vehicles), 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 vehicle is priced at 5 million yuan, and all vehicles produced within the year can be sold out that year.
(1) Find the profit function $L(x)$ (million yuan) for the year in terms of the annual production $x$ (hundreds of vehicles); (Profit = Sales - Cost)
(2) In 2018, when the production volume was how many hundreds of vehicles, the company's profit was the highest? And find the maximum profit.

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