
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 vehicles with new energy vehicles, China is vigorously implementing a plan that will reshape the global automotive industry. In 2020, a certain company plans to introduce new energy vehicle production equipment. Through market analysis, it is determined that a fixed cost of 300 million yuan needs to be invested throughout the year. An additional cost of y (in thousand yuan) is required for producing x (hundreds of vehicles), and y is defined as follows:
\[y=\left\{\begin{array}{l}{10{x}^{2}+100x,0<x<40}\\{501x+\frac{10000}{x}-4500,x\geq 40}\end{array}\right.\]
According to market research, each vehicle is priced at 50,000 yuan, and all vehicles produced within the year can be sold.

1. Find the function relationship of the profit S (in thousand yuan) in 2020 with the annual output x (in hundreds of vehicles). (Profit = Revenue - Cost)
2. When the production volume in 2020 is how many hundreds of vehicles, the company will make the maximum profit? And find the maximum profit.

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