
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
A company has an annual fixed cost of $250 million for producing a certain product. When the annual production volume is $x$ thousand units, an additional cost of $C(x)$ is required. When the annual production volume is less than 80 thousand units, $C(x)= \frac {1}{360}x^{3}+20x$ (million dollars); when the annual production volume is not less than 80 thousand units, $C(x)=51x+ \frac {10000}{x}-1450$ (million dollars). According to market analysis, all products can be sold when each unit is priced at $0.05 million.
(1) Write the annual profit function $L(x)$ (million dollars) with respect to the annual production volume $x$ (thousand units);
(2) What is the annual production volume (thousand units) that maximizes the profit from producing this product.

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