
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]

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[ACTION NAME]

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# Your action step 2

# Your action step 3

...

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Eradicating poverty is an important task for the government in caring for people's livelihoods, and understanding the actual income situation of residents is particularly important. Now, 100 farming households are randomly selected from a certain area to investigate the annual income and savings of each household for analysis. Let the annual income of the $i$-th household be $x_i$ (in ten thousand yuan), and the annual savings be $y_i$ (in ten thousand yuan). After data processing, we have $$\sum\limits_{i=1}^{100}x_{i}=500， \sum\limits_{i=1}^{100}y_{i}=100， \sum\limits_{i=1}^{100}x_{i}y_{i}=1000， \sum\limits_{i=1}^{100} x_{ i }^{ 2 }=3750$$．  
(Ⅰ) Given that a family's annual surplus $y$ is linearly related to the annual income $x$, find the linear regression equation;  
(Ⅱ) If the annual savings of a household in this area exceed 50,000 yuan, it is considered that the household has reached a well-off life. Please predict the minimum annual income required for a household to achieve a well-off life in ten thousand yuan?  
Note: In $$\hat{y} = \hat{b}x + \hat{a}$$, $$\hat{b} = \frac { \sum\limits_{i=1}^{n}x_{i}y_{i}-n \bar{x} \bar{y}}{ \sum\limits_{i=1}^{n}x_{ i }^{ 2 }-n \bar{x}^{2}}$$, $$\hat{a} = \bar{y} - \hat{b} \bar{x}$$, where $\bar{x}, \bar{y}$ are the sample means.

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