
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
Regarding the function $f(x) = \lg(|x| + 1)$ ($x \in \mathbb{R}$), the following statements are made:
1. The graph of $y = f(x)$ is symmetric about the y-axis;
2. In the interval $(-\infty, 0)$, the function $y = f(x)$ is increasing;
3. The minimum value of $f(x)$ is 0.

Among these statements, the correct statement numbers are.

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