
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]


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A factory produces a certain product with an annual fixed cost of $250 million. When producing $x$ million units, an additional cost of $C(x)$ million is required. When the annual production volume is less than 80 million units, $C(x)= \frac {1}{3}x^{2}+10x$; when the annual production volume is not less than 80 million units, $C(x)=51x+ \frac {10000}{x}-1450$. Assume that each unit of the product is sold for $50 million and all produced units can be sold that year.
1. Write out the annual profit $L(x)$ (million) as a function of the annual production volume $x$ (million units).
2. What is the production volume when the factory's profit from producing this product is the highest? What is the maximum profit?

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