
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 $f(x) = \log \frac{x^2 + 1}{|x|}$ ($x \neq 0$), the following statements are given:  
① Its graph is symmetric about the y-axis;  
② When $x > 0$, $f(x)$ is an increasing function; when $x < 0$, $f(x)$ is a decreasing function;  
③ $f(x)$ is an increasing function on the intervals $(-1, 0)$ and $(2, +\infty)$;  
④ The minimum value of $f(x)$ is $\log 2$;  
⑤ $f(x)$ has neither a maximum nor a minimum value.  
The correct sequence numbers are \_\_\_\_\_\_.

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