
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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# Your action step 3

...

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To promote the popularization of new energy vehicles, a city gradually increases the construction of charging infrastructure. The city has compiled statistics on the number of new energy vehicle charging stations over the past five years (unit: units), as shown in the table below:

| Year Number $x$ | 1 | 2 | 3 | 4 | 5 |
|-----------------|---|---|---|---|---|
| Year | 2018 | 2019 | 2020 | 2021 | 2022 |
| Number of New Energy Vehicle Charging Stations $y$ (units) | 37 | 104 | 147 | 186 | 226 |

$(1)$ It is known that a linear regression model can be used to fit the relationship between $y$ and $x$. Please explain using the correlation coefficient.

$(2)$ Find the linear regression equation for $y$ with respect to $x$ and predict the number of new energy vehicle charging stations in the city in 2026.

Reference data: $\sum_{i=1}^{5}{y_{i}}=700, \sum_{i=1}^{5}{x_{i}y_{i}}=2560, \sqrt{\sum_{i=1}^{5}{(y_{i}-\overline{y})^{2}}}\approx146.51, \sqrt{10}\approx3.16$.

Reference formulas: Correlation coefficient $r=\frac{\sum_{i=1}^{n}{(x_{i}-\overline{x})}(y_{i}-\overline{y})}{\sqrt{\sum_{i=1}^{n}{(x_{i}-\overline{x})^{2}}\sum_{i=1}^{n}{(y_{i}-\overline{y})^{2}}}$, regression equation $\hat{y}=\hat{b}x+\hat{a}$ where the least squares estimates of the slope and intercept are respectively $\hat{b}=\frac{\sum_{i=1}^{n}{(x_{i}-\overline{x})}(y_{i}-\overline{y})}{\sum_{i=1}^{n}{(x_{i}-\overline{x})^{2}}}, \hat{a}=\overline{y}-\hat{b}\overline{x}$.

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