
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
Which of the following statements are correct? $(Fill in the correct statement number)$.

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

② If the variance of sample data $x_{1}$, $x_{2}$, $\ldots$, $x_{10}$ is $4$, then the standard deviation of the data $2x_{1}+1$, $2x_{2}+1$, $\ldots$, $2x_{10}+1$ is $4$;

③ Given a random variable $X\sim N(1, \sigma ^{2})$, and $P(X > 3) = 0.2$, then $P(1 < X \leq 3) = 0.3$;

④ If the absolute value of the linear correlation coefficient $|r|$ is closer to $1$, then the linear correlation between the two variables is weaker;

⑤ $k^{2}$ is a random variable used to determine the correlation between two categorical variables. When the value of $k^{2}$ is small, it can be inferred that the two variables are not correlated.

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