
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]

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[ACTION NAME]

# Your action step 1

# Your action step 2

# Your action step 3

...

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system
At the 75th United Nations General Assembly, China pledged to adopt more effective policies and measures to strive to peak carbon dioxide emissions before 2030 and achieve carbon neutrality (referred to as "dual carbon goals") before 2060. This demonstrates China's firm determination to address climate change, indicating that China's economic structure and economic and social operation methods will undergo profound changes, greatly promoting the clean and green transformation of China's industrial chain. New energy vehicles and electric vehicles are important strategic emerging industries that play a crucial role in achieving the "dual carbon goals." In order to understand the sales of electric vehicles in a certain region, an organization obtained a linear regression equation for the sales volume $y$ (in units of 10,000 vehicles) with respect to the year $x$ using the least squares method as $\hat{y}=4.7x-9495.2$. The variance of sales volume $y$ is ${S}_{y}^{2}=50$, and the variance of the year $x$ is ${S}_{x}^{2}=2$.
$(1)$ Calculate the correlation coefficient $r$ between $y$ and $x$, and based on this, determine the strength of the correlation between the sales volume of electric vehicles $y$ and the year $x$.
$(2)$ The organization also surveyed 100 car owners in the region regarding the gender and type of car purchased, with the data shown in the table below:

|         | Non-electric Cars | Electric Cars | Total |
|---------|-------------------|---------------|-------|
| Male    | 30                | 20            | 50    |
| Female  | 15                | 35            | 50    |
| Total   | 45                | 55            | 100   |

Can it be concluded with 99% confidence that the purchase of electric cars is related to gender?
$(3)$ Among the owners who purchased electric cars, a stratified sample of 11 people was selected based on gender, and then 2 people were randomly selected from these 11 people. Let $X$ be the number of males among these 2 people. Find the probability distribution and mathematical expectation of $X$.
Reference formulas:
$(i)$ Linear regression equation: $\hat{y}=\hat{b}x+a$, where $\hat{b}=\frac{\sum_{i=1}^{n}{({x}_{i}-\overline{x})}({y}_{i}-\overline{y})}{\sum_{i=1}^{n}{{({x}_{i}-\overline{x})}^{2}}},a=\overline{y}-\hat{b}\overline{x}$;
$(ii)$ Correlation coefficient: $r=\frac{\sum_{i=1}^{n}{({x}_{i}-\overline{x})}({y}_{i}-\overline{y})}{\sqrt{\sum_{i=1}^{n}{{({x}_{i}-\overline{x})}^{2}}\sum_{i=1}^{n}{{({y}_{i}-\overline{y})}^{2}}}}$, if $r \gt 0.9$, it can be judged that $y$ and $x$ are strongly linearly related;
$(iii)$ ${\chi}^{2}=\frac{n(ad-bc)^{2}}{(a+b)(c+d)(a+c)(b+d)}$, where $n=a+b+c+d$.
Table:
| $\alpha $ | 0.100 | 0.050 | 0.010 | 0.001 |
|-----------|-------|-------|-------|-------|
| $x_{\alpha }$ | 2.706 | 3.841 | 6.635 | 10.828 |

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