
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
In response to the national call for "entrepreneurship and innovation for everyone," Xiao Wang decided to start a business in his field after graduating from college. After market research, Xiao Wang found that the annual fixed cost for producing a certain small electronic product is 20,000 yuan, and the variable cost C(x) in ten thousands yuan for producing x ten thousands units is given as follows: $$C(x)= \frac {1}{3}x^{2}+2x$$ for annual production less than 80,000 units, and $$C(x)=7x+ \frac {100}{x}-37$$ for annual production of at least 80,000 units. Each product is sold for 6 yuan. It is assumed that all products produced by Xiao Wang are sold within the year.
(Ⅰ) Write the function expression P(x) for the annual profit in ten thousands yuan with respect to the annual production x in ten thousands units (Note: Annual profit = Annual sales income - Fixed cost - Variable cost);
(Ⅱ) At what annual production quantity (in ten thousands units) is Xiao Wang's profit maximized for this product, and what is the maximum profit?

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