
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 manufacturer plans to hold a promotional event in 2010. After investigation and calculation, the annual sales volume of the product (i.e., the factory's annual output $x$ in ten thousand units) and the annual promotional expenses $m$ (in ten thousand yuan) ($m\geqslant 0$) satisfy $x=3- \dfrac {k}{m+1}$ ($k$ is a constant). If no promotional activities are conducted, the annual sales volume of the product can only be 1 ten thousand units. It is known that the fixed investment for producing the product in 2010 is 80,000 yuan, and an additional investment of 160,000 yuan is required for every ten thousand units produced. The factory sets the selling price of each product to 1.5 times the average annual cost per product (the product cost includes both fixed and additional investments).  
(1) Express the profit $y$ (in ten thousand yuan) in 2010 as a function of the annual promotional expenses $m$ (in ten thousand yuan);  
(2) How much should the factory invest in promotional expenses in 2010 to maximize its profit?

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