
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 $\sum_{i=1}^{10}{{{x}\_{i}}}=80$, $\sum_{i=1}^{10}{{{y}\_{i}}}=20$, $\sum_{i=1}^{10}{{{x}\_{i}}{{y}\_{i}}}=184$, $\sum_{i=1}^{10}{{{x}\_{i}}^{2}}=720$.

(I) Find the linear regression equation $\widehat{y}=\widehat{b}x+\widehat{a}$ of monthly savings $y$ on monthly income $x$;

(II) Predict the monthly savings of a household in this residential area with a monthly income of $7$ thousand yuan.

Note: In the linear regression equation $\widehat{y}=\widehat{b}x+\widehat{a}$, $\widehat{b}=\frac{\sum_{i=1}^{n}{{{x}\_{i}}{{y}\_{i}}}-n\overline{x}\overline{y}}{\sum_{i=1}^{n}{x\_{i}^{2}}-n{{\overline{x}}^{2}}}$, $\widehat{a}=\overline{y}-\widehat{b}\overline{x}$, where $\bar{x},\bar{y}$ are the sample means.

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