
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
To investigate the relationship between monthly income and monthly savings of households in a residential area, 10 households were randomly selected from the area. The monthly income $x_i$ (in thousands of yuan) and monthly savings $y_i$ (in thousands of yuan) of the $i$-th household were obtained, with $\sum\limits_{i=1}^{10} x_i = 80$, $\sum\limits_{i=1}^{10} y_i = 20$, $\sum\limits_{i=1}^{10} x_i y_i = 184$, and $\sum\limits_{i=1}^{10} x_i^2 = 720$. Using the following formulas as a reference: $$\begin{cases} \hat{b} = \frac{\sum\limits_{i=1}^{10} x_i y_i - n \bar{x} \bar{y}}{\sum\limits_{i=1}^{n} x_i^2 - n \bar{x}^2} \\ \hat{a} = \bar{y} - \hat{b} \bar{x} \end{cases}$$
(1) Find the linear regression equation of monthly savings $y$ on monthly income $x$.
(2) Predict the monthly savings for a household with a monthly income of 8 thousand yuan.

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