
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]


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In recent years, short video social apps have been increasingly popular, allowing users to select songs, shoot music videos, and create their own works. A user conducted an analysis on the relationship between the number of short videos $x$ they posted and the sum of likes received $y$. The data obtained is as follows:

| $x$ | $3$ | $4$ | $5$ | $6$ | $7$ |
|-----|-----|-----|-----|-----|-----|
| $y$ | $45$ | $50$ | $60$ | $65$ | $70$ |

$(Ⅰ)$ Calculate the correlation coefficient $r$ between $x$ and $y$, and determine if it can be considered that there is a high degree of linear correlation between the number of short videos posted and the sum of likes received. (If $0.3 \lt |r| \lt 0.75$, the linear correlation is considered moderate; if $|r| \gt 0.75$, the linear correlation is considered high. Calculate $r$ with a precision of $0.01$).

$(Ⅱ)$ Find the linear regression equation of $y$ with respect to $x.

Reference data: $\sum_{i=1}^5{{{({{x_i}-\overline{x}})}^2}}=10$, $\sum_{i=1}^5{{{({{y_i}-\overline{y}})}^2}}=430$, $\sum_{i=1}^5{({{x_i}-\overline{x}})({{y_i}-\overline{y}})}=65$, $\sqrt{4300}≈65.57$.

Correlation coefficient formula: $r=\frac{{\sum_{i=1}^n{({{x_i}-\overline{x}})({{y_i}-\overline{y}})}}}{{\sqrt{\sum_{i=1}^n{{{({{x_i}-\overline{x}})}^2}}}\sqrt{\sum_{i=1}^n{{{({{y_i}-\overline{y}})}^2}}}}}$.

Regression line equation slope $\hat{b}=\frac{{\sum_{i=1}^n{({{x_i}-\overline{x}})({{y_i}-\overline{y}})}}}{{\sum_{i=1}^n{{{({{x_i}-\overline{x}})}^2}}}}$, intercept $\hat{a}=\overline{y}-\hat{b}\overline{x}$.

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