
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
Given a set of sample data $(x\_1, y\_1)$, $(x\_2, y\_2)$, ..., $(x\_n, y\_n)$, the regression line equation is $\hat{y} = bx + a$. The correct statement(s) is/are\_ \_\_\_\_\_\_.

(1) The line $\hat{y} = bx + a$ must pass through the point $(\bar{x}, \bar{y})$
(2) The line $\hat{y} = bx + a$ passes through at least one of the points $(x\_1, y\_1)$, $(x\_2, y\_2)$, ..., $(x\_n, y\_n)$
(3) The slope of the line $\hat{y} = bx + a$ is $\frac{\sum\_{i=1}^{n} x\_i y\_i - n \bar{x} \cdot \bar{y}}{\sum\_{i=1}^{n} x\_i^2 - n \bar{x}^2}$
(4) The regression line equation $\hat{y} = bx + a$ best represents the linear relationship between $x$ and $y$ in the sample data. When $b > 0$, $x$ and $y$ are positively correlated, and when $b < 0$, $x$ and $y$ are negatively correlated.

Note: Related data
$$
\begin{cases}
\hat{b} = \frac{\sum\_{i=1}^{n} (x\_i - \bar{x})(y\_i - \bar{y})}{\sum\_{i=1}^{n} (x\_i - \bar{x})^2} = \frac{\sum\_{i=1}^{n} x\_i y\_i - n \bar{x} \bar{y}}{\sum\_{i=1}^{n} x\_i^2 - n \bar{x}^2} \
\hat{a} = \bar{y} - \hat{b} \bar{x}
\end{cases}
$$
where $\bar{x} = \frac{1}{n} \sum\_{i=1}^{n} x\_i$, $\bar{y} = \frac{1}{n} \sum\_{i=1}^{n} y\_i$.

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