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[ASSESS]

[ADVANCE]

[VERIFY]

[SIMPLIFY]

[SYNTHESIZE]

[PIVOT]

[OUTPUT]

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[ACTION NAME]

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# Your action step 2

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...

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A manufacturer plans to hold a promotion event, and after conducting a survey and calculations, the annual sales volume x (in ten thousand units) and the annual promotion expense m (in ten thousand yuan) meet the relation x = 3 - $$\frac{k}{m+1}$$ (where k is a constant). If no promotion event is held, the annual sales volume will only be 1 ten thousand units. It is known that the fixed input for producing the product is 80,000 yuan, and producing every ten thousand units of the product requires an input of 160,000 yuan. The manufacturer sets the price of each unit to be 1.5 times the average annual per-unit cost of the product (the product cost includes fixed input and additional input, but not the promotion expense).
1. Express the annual profit y (in ten thousand yuan) as a function of the annual promotion expense m (in ten thousand yuan).
2. At what annual promotion expense m will the manufacturer's annual profit be maximized? What is the maximum annual profit in ten thousand yuan?

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