
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 random sample of $10$ households was taken from a residential area, and the monthly income $x_{i}$ (in thousand yuan) and monthly savings $y_{i}$ (in thousand yuan) of the $i$-th household were obtained. It was calculated that $\sum_{i=1}^{10}{{{x}\_{i}}}=80$, $\sum_{i=1}^{10}{{{y}\_{i}}}={20}$, $\sum_{i=1}^{10}{{{x}\_{i}}}{{y}\_{i}}=184$, $\sum_{i=1}^{10}{x\_{i}^{2}}=720$.

1. Find the linear regression equation $\widehat{y}=\widehat{b}x+\widehat{a}$ of the monthly savings $y$ on the monthly income $x$;
2. Determine whether the variables $x$ and $y$ are positively or negatively correlated;
3. Predict the monthly savings of a household in this residential area with a monthly income of $7$ thousand yuan.

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