
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

...

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With the continuous development of technology, "smartphones" have become an indispensable necessity in people's lives. The table below shows the annual total shipment of mobile phones in a certain city in Guangxi (unit: ten thousand units).

| Year | 2018 | 2019 | 2020 | 2021 | 2022 |
|------|------|------|------|------|------|
| Year Code $x$ | 1 | 2 | 3 | 4 | 5 |
| Total Shipment $y$ (ten thousand units) | 4.9 | 4.1 | 3.9 | 3.2 | 3.5 |

And the calculated value of $\sum_{i=1}^5{({{x_i}-\overline{x}})}({{y_i}-\overline{y}})=-3.7$.

$(1)$ It is known that the total shipment of mobile phones $y$ in the city can be fitted with a linear regression model with the year code $x$. Find the linear regression equation of $y$ with respect to $x$.

$(2)$ Predict the total shipment of mobile phones in the city in 2023.

Given: The formulas for the least squares estimates of the slope and intercept in the linear regression equation $\hat{y}=\hat{a}+\hat{b}x$ 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 $\hat{a}=\overline{y}-\hat{b}\overline{x}$.

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