
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
The following are four statements:
1. Use the correlation coefficient $R^{2}$ to describe the regression effect. The smaller the $R^{2}$, the better the model's fitting effect.
2. The negation of proposition $P$: "There exists $x_{0} \in \mathbb{R}$, such that $x_{0}^{2} - x_{0} - 1 > 0$" is $\neg P$: "For all $x \in \mathbb{R}$, $x^{2} - x - 1 \leqslant 0$".
3. Let the random variable $X$ follow the normal distribution $N(0,1)$. If $P(x > 1) = p$, then $P(-1 < X < 0) = \frac{1}{2} - p$.
4. The regression line must pass through the center of the sample points $(\bar{x}, \bar{y})$.

Among these statements, the correct ones are __________ (Please fill in all the correct statement numbers on the line).

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