
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
New energy vehicles have the advantages of saving fuel energy, reducing exhaust emissions, and effectively protecting the environment. According to statistics, as of the end of September 2022, the number of new energy vehicles in China is 1149 million, accounting for 3.65% of the total number of vehicles. Xiao Yang plans to buy a new energy vehicle for 90,000 yuan as a taxi (for no other use). According to market research, the total expenditure for using this car for $n$ ($n\in \mathbb{N}^{*}$, $n\leqslant 8$) years is $(0.25n^{2}+0.25n)$ million yuan, and the annual income is 5.25 million yuan.  
$(1)$ From which year does this car start to make a profit?  
$(2)$ How many years should this car be used to be most cost-effective?  
(Note: ① Profit = Income - Expenditure; ② The most cost-effective scrapping year for a taxi generally refers to the number of years of use when the average annual profit is maximized.)

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