
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
A certain fee-based app (mobile application) has been loved by users since its launch due to its simple interface design, convenient operation, and powerful practical functions. The company that owns the app has compiled a data table of the amount $x$ (in units of yuan) of monthly rent reduction for users and the corresponding number of users $y$ (in units of ten thousand people) in a month. The data is as follows:

| Amount of Monthly Rent Reduction $x$ (yuan) | $4$ | $5$ | $6$ | $7$ | $8$ |
|--------------------------------------------|-----|-----|-----|-----|-----|
| Number of Users $y$ (ten thousand people)  | $2$ | $2.1$ | $2.5$ | $2.9$ | $3.2$ |

It is known that $x$ and $y$ are linearly related.

$(1)$ Find the empirical regression equation of $y$ with respect to $x$ ($\sum_{i=1}^5{x_i^2}=190$, $\sum_{i=1}^5{{x_i}{y_i}}=79.4$);

$(2)$ Based on this, predict how many users there will be in a month when the monthly rent reduction is $14$ yuan.

Reference formula: For a set of data $(x_{i}$, $y_{i})\left(i=1,2,\ldots ,n\right)$ with a linear relationship, the least squares estimates of the slope and intercept of the empirical regression line $\hat{y}=\hat{b}x+\hat{a}$ are respectively $\hat{b}=\frac{{\sum_{i=1}^n{({{x_i}-\overline{x}})}({{y_i}-\overline{y}})}}{{\sum_{i=1}^n{{{({{x_i}-\overline{x}})}^2}}}}=\frac{{\sum_{i=1}^n{{x_i}{y_i}}-n\overline{x}\overline{y}}}{{\sum_{i=1}^n{x_i^2}-n{{\overline{x}}^2}}}$, $\hat{a}=\overline{y}-\hat{b}\overline{x}$.

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