
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
On May 17, 2023, the 318th zero-kilometer self-driving camp of the Sichuan-Tibet line was launched in the Rain City District, and the "5.17 I want to ride" Ya'an Station event kicked off. The 318th zero-kilometer self-driving camp of the Sichuan-Tibet line once again became the focus of attention. The project is guided by the culture of "driving 318 in this life, first stop in Ya'an" and "the third pole of the world, zero kilometers in Ya'an," utilizing the transportation location and brand resources of Ya'an to innovate and create attractive experiential projects, enhancing the discourse power and influence of the Ya'an-Tibet tour. A cycling enthusiast recently conducted a statistical analysis of the cycling situation under the guidance of professionals. The comprehensive physical index score $x$ during each cycling period and the corresponding time $y$ (unit: hours) are shown in the table below:

| Physical Index Score ($x$) | 1   | 2   | 3   | 4   | 5   |
|---------------------------|-----|-----|-----|-----|-----|
| Time ($y$ / hours)        | 9.5 | 8.6 | 7.8 | 7   | 6.1 |

$(1)$ Based on the data in the table, a linear regression model can be used to fit the relationship between $y$ and $x$. Please explain using the correlation coefficient.  
$(2)$ Establish the regression equation of $y$ with respect to $x$.  
Reference data and formulas: Correlation coefficient $r = \frac{\sum_{i=1}^{n}{(x_{i}-\overline{x})(y_{i}-\overline{y})}}{\sqrt{\sum_{i=1}^{n}{(x_{i}-\overline{x})^{2}}\sum_{i=1}^{n}{(y_{i}-\overline{y})^{2}}}}$, $\hat{b} = \frac{\sum_{i=1}^{n}{(x_{i}-\overline{x})(y_{i}-\overline{y})}}{\sum_{i=1}^{n}{(x_{i}-\overline{x})^{2}}}$, $\hat{a} = \overline{y} - \hat{b}\overline{x}$, $\sqrt{7060} \approx 84$.

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