
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 the function $y=f(x)$, where $x\in\mathbb{R}$, consider the following statements:
1. If for any $x_1, x_2 \in \mathbb{R}$ with $x_1 \neq x_2$, it holds that $$\frac{f(x_2) - f(x_1)}{x_2 - x_1} < 0$$, then $f(x)$ is a decreasing function on $\mathbb{R}$.
2. If $f(x)$ is an even function on $\mathbb{R}$, and it is a decreasing function on $(-\infty, 0)$, and $f(-2) = 0$, then the solution set of $f(x) > 0$ is $(-2, 2)$.
3. If $f(x)$ is an odd function on $\mathbb{R}$, then $y=f(x) - f(|x|)$ is also an odd function on $\mathbb{R}$.
4. If there exists a constant $t$ such that for any $x$, $f(x-t) = f(x+t)$, then the graph of $f(x)$ is symmetric about the line $x=t$.

The correct statements are __________ .

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