
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
To increase the annual production of a product, a company plans to carry out technical reforms in 2014. Through investigation and calculation, it was found that the annual production $x$ (in ten thousand pieces) and the investment $m$ (in ten thousand yuan) in technical reforms satisfy the equation $x = 3 - \frac{k}{m+1}$ (where $k$ is a constant). If no technological reform is undertaken, the production of the product can only reach one ten thousand pieces that year. It is known that the fixed investment for producing the product in 2014 is 80 thousand yuan, and producing each ten thousand pieces of the product requires an additional investment of 160 thousand yuan. Due to good market conditions, all products produced by the factory can be sold. The factory sets the selling price of each product at 1.5 times the production cost (including both fixed investment and additional investment).  
(1) Express the profit $y$ (in ten thousand yuan) of the product in 2014 as a function of the technical reform investment $m$ (in ten thousand yuan);  
(2) How much should the company invest in technical reforms in 2014 to maximize the profit?

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