
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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In response to the national call for "mass entrepreneurship and innovation," Little Li decided to start his own business after graduation, utilizing his professional knowledge. After market research, it was found that producing a certain type of small electronic product requires an annual fixed cost of 50,000 yuan, and an additional investment in variable cost of C(x) yuan is needed for producing x ten thousand units, where $$C(x)= \begin{cases} \frac {1}{2}x^{2}+4x，0＜x＜8 \\ 11x+ \frac {49}{x}-35，x≥8\end{cases}$$. Each unit is sold for 10 yuan, and all products can be sold out within the year.

1. Write the analytical expression for the annual profit P(x) (ten thousand yuan) in terms of the annual production volume x (ten thousand units). (Note: annual profit = annual sales revenue - fixed cost - variable cost)
2. What is the annual production volume (ten thousand units) that maximizes Little Li's profit in this product's production? What is the maximum profit?

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