
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
Randomly select 10 families from a residential area, and obtain the data of the monthly income $x_i$ (unit: thousand yuan) and monthly savings $y_i$ (unit: thousand yuan) of the $i$-th family. It is calculated that $$\sum\limits_{i=1}^{10}x_{i}=80$$, $$\sum\limits_{i=1}^{10}y_{i}=20$$, $$\sum\limits_{i=1}^{10}x_{i}y_{i}=184$$, $$\sum\limits_{i=1}^{10} x_{ i }^{ 2 }=720$$.  
(Ⅰ) Find the linear regression equation of family monthly savings $y$ on monthly income $x$, $\hat{y}= \hat{b}x+ \hat{a}$;  
(Ⅱ) Determine whether the variables $x$ and $y$ are positively or negatively correlated;  
(Ⅲ) If the monthly income of a family in this residential area is 12 thousand yuan, predict the monthly savings of this family.  
Note: In the linear regression equation $\hat{y}= \hat{b}x+ \hat{a}$, $$\hat{b}= \frac { \sum\limits_{i=1}^{n}x_{i}y_{ i }-n \overline {x} \overline {y}}{ \sum\limits_{i=1}^{n} x_{ i }^{ 2 }-n \overline {x}^{2}}$$, $$\hat{a}= \overline {y}- \hat{b} \overline {x}$$．Here, $\overline {x}$, $\overline {y}$ are the sample means, and the linear regression equation can also be written as $\land y$ = $\land b$x + $\land a$.

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