
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
Define the even function $f(x)$ on $\mathbb{R}$. When $x \in [1,2]$, $f(x) < 0$, and $f(x)$ is an increasing function. Consider the following four statements:

1. $f(x)$ is increasing on $[-2,-1]$;
2. When $x \in [-2,-1]$, $f(x) < 0$;
3. $f(x)$ is decreasing on $[-2,-1]$;
4. $|f(x)|$ is decreasing on $[-2,-1]$.

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

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