
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 for its products in 2016. After investigation and estimation, the annual sales volume $m$ (in ten thousand units) and the annual promotional expenses $x$ (in ten thousand yuan) satisfy the relationship: $m=3- \frac{2}{x+1}$. It is known that the fixed investment for producing the product in 2016 is 80,000 yuan, and an additional investment of 160,000 yuan is required for every ten thousand units produced. The manufacturer's production volume equals its sales volume, and the sales revenue is 1.5 times the production cost (the production cost consists of fixed investment and additional investment).
(1) Express the profit $y$ (in ten thousand yuan) in 2016 as a function of the annual promotional expenses $x$ (in ten thousand yuan);
(2) How much should the manufacturer invest in promotional expenses in 2016 to maximize its profit?

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