
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
In recent years, China's new energy industry has made remarkable achievements. In the "Development Plan for the New Energy Vehicle Industry (2021-2035)" officially released by the State Council in 2020, it was proposed that by 2025, the sales volume of new energy vehicles would account for about 20% of the total sales of new vehicles. Efforts are being made to make pure electric vehicles the mainstream of new vehicle sales after 15 years of continuous efforts. Against this backdrop, the stock of new energy vehicles in a certain city has been continuously increasing. The relevant department has conducted statistics on the stock of new energy vehicles in the city from 2018 to 2022, denoted as $y$ (unit: ten thousand vehicles), with respect to the year code $t$ (where $t=1$ represents the year 2018). The statistical table of $y$ and $t$ is as follows:

| $t$ | 1 | 2 | 3 | 4 | 5 |
|-----|---|---|---|---|---|
| $y$ | 1.5 | 3.2 | 4 | 5.3 | 6 |

$(1)$ Please calculate the correlation coefficient $r$ to demonstrate that $y$ and $t$ have a strong linear relationship. (If $|r| > 0.75$, the variables have a strong linear relationship.)  
$(2)$ Find the linear regression equation and predict the stock of new energy vehicles in 2023.

Given 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: $\hat{y}=\hat{a}+\hat{b}x$, where the least squares estimates of the slope and intercept are $\hat{b}=\frac{\sum_{i=1}^n{({{x_i}-\overline{x}})}({{y_i}-\overline{y}})}{\sum_{i=1}^n{{{({{x_i}-\overline{x}})}^2}}}$ and $\hat{a}=\overline{y}-\hat{b}\overline{x}$.  
Given data: $\sum_{i=1}^5{{{({{t_i}-\overline{t}})}^2}}=10$, $\sum_{i=1}^5{{{({{y_i}-\overline{y}})}^2}}=12.58$, $\sum_{i=1}^5{({{t_i}-\overline{t}})}({{y_i}-\overline{y}})=11.1$, $\sqrt{125.8}\approx 11.22$.

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