
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
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 of electric vehicle sales $y$ (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 $y$ 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 electric vehicle sales $y$ and the year $x$.
$(2)$ The organization also surveyed 100 car owners in the region on gender and the type of car purchased, with the data shown in the table below:

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

Can it be considered 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 by gender, and then 4 people were randomly selected from these 11 people. Let $X$ be the number of males among these 4 people. Find the probability distribution and mathematical expectation of $X$.

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