
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 county is economically active and holds a traditional cultural folk festival. Xiao Zhang set up a booth to catch small white rabbits. Let $x_{i}$ represent the average temperature of the $i$-th day, $y_{i}$ represent the number of people participating in the activity on the $i$-th day, where $i=1, 2, \ldots, 20$. According to statistics, the following values of some statistical quantities are calculated: $\sum_{i=1}^{20}{(x_{i}-\overline{x})^2}=80$, $\sum_{i=1}^{20}{(y_{i}-\overline{y})^2}=9000$, $\sum_{i=1}^{20}(x_{i}-\overline{x})(y_{i}-\overline{y})=800$.  
$(Ⅰ)$ Based on the given data, determine whether a linear regression model can be used to fit the relationship between $y$ and $x$ using the correlation coefficient $r$ (rounded to $0.01$).  
$(Ⅱ)$ Now, two families are participating in catching the rabbits. Family $A$ has 3 members, each with a probability of $\frac{3}{10}$ to catch a small white rabbit in each round. Family $B$ has 3 members with probabilities of $\frac{1}{3}$, $\frac{1}{4}$, and $\frac{1}{6}$ to catch a rabbit in each round. Each family's 3 members play one round of catching the rabbit, with each person charged $20 yuan per round. The value of each small white rabbit is $40 yuan. The catching of each rabbit by a person is independent of others. The decision is based on the expected profit of each family. After one round, which family suffers greater losses?  
Correlation coefficient formula: $r=\frac{\sum_{i=1}^{n}({x}_{i}-\overline{x})({y}_{i}-\overline{y})}{\sqrt{\sum_{i=1}^{n}({{x}_{i}-\overline{x})}^{2}\sum_{i=1}^{n}({y}_{i}-\overline{y})^{2}}$.

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