
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
Determine the correct statements from the following options.

(1) The regression line $\hat{y}=\hat{b}x+\hat{a}$ always passes through the center of the sample points $(\bar{x}, \bar{y})$, and passes through at least one sample point;

(2) Adding the same constant to each data point in a dataset does not change the variance;

(3) Use the correlation coefficient $R^2$ to evaluate the regression effect; the closer it is to $1$, the better the model's fit;

(4) If the observed value $K$ of the random variable ${K}^{2}$ of the categorical variables $X$ and $Y$ is larger, then the credibility of "$X$ is related to $Y$" is smaller;

(5) For the independent variable $x$ and the dependent variable $y$, when $x$ takes a definite value, $y$'s value has some randomness. The uncertain relationship between $x$ and $y$ is called a functional relationship;

(6) If the residual points in the residual plot are more evenly distributed in the horizontal band area, it indicates that the selected model is more appropriate;

(7) The model with smaller residual squared sum has a better fitting effect.

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