
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 families from a residential area was taken to obtain the monthly income $x_i$ (unit: thousand yuan) and monthly savings $y_i$ (unit: thousand yuan) data for the $i$-th family. It was calculated that $\sum\limits_{i=1}^{10}{{x_i}=80}$, $\sum\limits_{i=1}^{10}{{y_i}=20}$, $\sum\limits_{i=1}^{10}{{x_i}{y_i}=184}$, $\sum\limits_{i=1}^{10}{x_i^2}=720.$ (Note: $\widehat{b}=\dfrac{\sum\limits_{i=1}^{n}{{x_i}{y_i}-n\overline{x}\overline{y}}}{\sum\limits_{i=1}^{n}{x_i^2-n{{\overline{x}}^2}}}$, $\widehat{a}=\overline{y}-\widehat{b}\overline{x}$)

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

(2) Determine whether the variables $x$ and $y$ are positively or negatively correlated;

(3) If a family in this residential area has a monthly income of 7 thousand yuan, predict the family's monthly savings.

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