
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]

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...

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Wearing a helmet is a responsible behavior for both families and society. A certain city continuously conducts safety education on this matter. The table below shows the statistical data of drivers not wearing helmets captured by surveillance equipment at a main intersection in the city for $4$ consecutive years:

| Year | $2018$ | $2019$ | $2020$ | $2021$ |
|------|--------|--------|--------|--------|
| Year Number $x$ | $1$ | $2$ | $3$ | $4$ |
| Number of People Not Wearing Helmets $y$ | $1150$ | $1000$ | $900$ | $750$ |

$(1)$ Please use the given data to find the regression line equation between the number of people not wearing helmets $y$ and the year number $x$, $\hat{y}=\hat{b}x+\hat{a}$;  
$(2)$ Estimate the number of people not wearing helmets at this intersection in the year $2022$.  
Reference formula: $\hat{b}=\frac{{\sum_{i=1}^n{{x_i}}{y_i}-n\overline{x}\overline{y}}}{{\sum_{i=1}^n{x_i^2-n{{\overline{x}}^2}}}}=\frac{{\sum_{i=1}^n{({x_i}-\overline{x})}({y_i}-\overline{y})}}{{\sum_{i=1}^n{{{({{x_i}-\overline{x}})}^2}}}},\hat{a}=\overline{y}-\hat{b}\overline{x}$.

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