
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 $f(x) = \lg \frac{x^2 + 1}{|x|}$ where $x \neq 0$ and $x \in \mathbb{R}$. The following statements are given:

1) The graph of $y = f(x)$ is symmetric about the $y$-axis.
2) The function $y = f(x)$ is decreasing in the interval $(-\infty, 0)$.
3) The minimum value of $f(x)$ is $\lg 2$.
4) The function $f(x)$ is increasing in the interval $(1, +\infty)$.

Determine the correct statement(s).

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