
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]


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According to the statistics from the National Bureau of Statistics, the number of newborns in China from $2018$ to $2022$ is as follows:

| Year Number $x$ | 1    | 2    | 3    | 4    | 5    |
|------------------|------|------|------|------|------|
| Year             | 2018 | 2019 | 2020 | 2021 | 2022 |
| Newborns $y$ (in 10,000s) | 1523 | 1465 | 1200 | 1062 | 956  |

$(1)$ Based on the data in the table, a linear regression model can be used to fit the relationship between the number of newborns $y$ and the year number $x$. Please explain using the correlation coefficient.

$(2)$ Establish the regression equation of $y$ with respect to $x$ and predict the number of newborns in China in $2023$.

Reference formula and data: $r=\frac{{\sum_{i=1}^n{{x_i}{y_i}}-n\overline{x}\overline{y}}}{{\sqrt{({\sum_{i=1}^n{x_i^2}-n{{\overline{x}}^2}})({\sum_{i=1}^n{y_i^2}-n{{\overline{y}}^2}})}}$, $\hat{b}=\frac{{\sum_{i=1}^n{{x_i}{y_i}}-n\overline{x}\overline{y}}}{{\sum_{i=1}^n{x_i^2}-n{{\overline{x}}^2}}}$, $\hat{a}=\overline{y}-\hat{b}\overline{x}$, $\sum_{i=1}^5{{y_i}}=6206$, $\sum_{i=1}^5{{x_i}{y_i}}=17081$, $\sqrt{({\sum_{i=1}^5{x_i^2}-5{{\overline{x}}^2}})({\sum_{i=1}^5{y_i^2}-5{{\overline{y}}^2}})}≈1564$.

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