
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
Consider the function $f(x) = \log \frac{x^2 + 1}{|x|}$ (where $x\neq 0$, $x \in \mathbb{R}$). The following statements are proposed:
① The graph of $f(x)$ is symmetric with respect to the y-axis.
② The minimum value of $f(x)$ is 2.
③ The function $f(x)$ is decreasing on $(-\infty, 0)$ and increasing on $(0, +\infty)$.
④ The function $f(x)$ does not have a maximum value.
Indicate the correct statement number(s).

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