
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 certain company invested $144$ million yuan in a thermal power generation project. The total maintenance cost for $n$ years $(n\in N_{+})$ is $(4n^{2}+40n)$ million yuan, and the project brings in an annual income of $100$ million yuan for the company. Assuming that by the end of the $n$th year, the net profit of the project is $y$ million yuan. (Net profit $=$ cumulative income $-$ total maintenance cost $-$ investment cost)<br/>$(1)$ Write down the expression for net profit $y$ and determine from which year the project starts to make a profit;<br/>$(2)$ With the rapid development of the solar photovoltaic industry in China, the cluster effect and continuous technological innovation have further reduced costs. After careful consideration, the company decided to invest in a solar power generation project. There are two options for dealing with the existing thermal power generation project:<br/>① When the average annual profit is maximized, the project will be sold for $12$ million yuan;<br/>② When the net profit is maximized, the project will be sold for $4$ million yuan.<br/>Which option do you think is most beneficial for the company's development? Please explain the reason.

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