
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
The wisdom and vitality of netizens have given rise to new business formats, such as online shopping, live streaming sales, and grocery shopping through mobile apps, which have entered our lives and changed our way of living. Along with this, the situation of telecommunications network fraud is also very serious. Therefore, the Ministry of Public Security has launched a national-level anti-fraud "bombshell" system - the "National Anti-Fraud Center App". This software can effectively prevent fraud and quickly report fraudulent content. Users can effectively avoid various online frauds by learning anti-fraud knowledge in the app, reducing unnecessary financial losses. After the launch of the "National Anti-Fraud Center App" in a certain province, various measures have been taken to actively promote the installation and registration of the "National Anti-Fraud Center App" throughout the province. According to statistics, the number of reported cases of online fraud in the province, denoted as $y$ (cases), is related to the promotion time and the data of the number of reported cases after $x$ months of promotion are recorded as follows:

| Promotion Months | 1 | 2 | 3 | 4 | 5 | 6 | 7 |
|------------------|---|---|---|---|---|---|---|
| $y$ (cases)      | 891 | 888 | 351 | 220 | 200 | 138 | 112 |

$(1)$ Using $y=a+\frac{b}{x}$ as the regression equation model, calculate the regression equation using the data in the table.  
$(2)$ Analyze whether continuously increasing the promotion efforts in the province could potentially reduce the number of reported cases of online fraud to near zero.  
Reference data (where $t_{i}=\frac{1}{x_i}$):

| $\sum_{i=1}^7{t_i}{y_i}$ | $\overline{t}$ | $\sum_{i=1}^7{t_i^2}-7×{\bar{t}^2}$ |
|-------------------------|---------------|-------------------------------------|
| 1586 | 0.37 | 0.55 |

Reference formula: For a set of data $(x_{1}$,$y_{1})$,$(x_{2}$,$y_{2})$,$(x_{3}$,$y_{3})\cdots $,$(x_{n}$,$y_{n})$, the least squares estimates of the slope and intercept of the regression line $y=\hat{b}x+\hat{a}$ are respectively: $\hat{b}=\frac{{\sum_{i=1}^n{{x_i}}{y_i}-n\overline{x}\overline{y}}}{{\sum_{i=1}^n{x_i^2}-n{{\overline{x}}^2}}}$, $\hat{a}=\overline{y}-\hat{b}\overline{x}$.

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