
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
To investigate the population of a certain species of wild animals in a specific area, the area is divided into 100 plots of similar size. From these plots, 10 plots are randomly selected as sample areas. The sample data $(x_{i}, y_{i})$ $(i=1,2,\ldots,10)$ is obtained from the survey, where $x_{i}$ and $y_{i}$ represent the plant coverage area (in hectares) and the number of this species of wild animals in the $i$-th sample area, respectively. It is analyzed that the number of wild animals $y$ is linearly related to the plant coverage area $x$, and the following calculations are obtained: $\sum_{i=1}^{10}{{x_i}}=30$, $\sum_{i=1}^{10}{{y_i}}=600$, $\sum_{i=1}^{10}{x_i^2}=250$, $\sum_{i=1}^{10}(x_{i}-\overline{x})(y_{i}-\overline{y})=400$.  
$(Ⅰ)$ Find the regression line equation for the plant coverage area and the number of wild animals in this area.  
$(Ⅱ)$ Based on the above equation, estimate the number of this species of wild animals in an area with a plant coverage area of 5 hectares.  
Reference formula: The least squares estimates of the slope and intercept in the regression line equation $\hat{y}=\hat{a}+\hat{b}x$ are respectively: $\hat{b}=\frac{\sum_{i=1}^{n}({x}_{i}-\overline{x})({y}_{i}-\overline{y})}{\sum_{i=1}^{n}({x}_{i}-\overline{x})^{2}}=\frac{\sum_{i=1}^{n}{x}_{i}{y}_{i}-n\overline{x}\cdot\overline{y}}{\sum_{i=1}^{n}{{x}_{i}}^{2}-n{\overline{x}}^{2}$, $\hat{a}=\overline{y}-\hat{b}\overline{x}$.

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