
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
Among the following statements, the correct ones are ______________. (Fill in the correct proposition numbers)

1. To characterize the regression effect, we use $R^2 = 1 - \frac{\sum_{i=1}^{n}(y_i - \hat{y}_i)^2}{\sum_{i=1}^{n}(y_i - \bar{y})^2}$. When $R^2$ is larger, the model's fitting effect is worse; conversely, it is better.

2. If a differentiable function $f(x)$ has an extreme value at $x=x_0$, then $f'(x_0)=0$.

3. Inductive reasoning is reasoning from specific to general, while deductive reasoning is reasoning from general to specific.

4. In mathematics, the synthetic method of proving problems is "from cause to effect", and the analytic method is "from effect to cause".

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