
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 plans to invest an appropriate amount of advertising expenses to promote its products. The expected sales Q (in ten thousand units) and the advertising expenses x (in ten thousand yuan) within a year have the function relationship of $Q= \frac {3x+1}{x+1}$ ($x\geq0$). It is known that the annual fixed investment for producing this product is 3 million yuan, and an additional investment of 32 million yuan is required for every ten thousand units produced. If the selling price per unit is the sum of "150% of the average production cost per unit" and "50% of the average advertising cost per unit per year".  
(1) Try to express the annual profit W (in ten thousand yuan) as a function of the annual advertising expenses x (in ten thousand yuan);  
(2) How much should the annual advertising expenses be to maximize the company's annual profit? What is the maximum profit?

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