
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 $f(x) = \lg \frac{x}{x^2+1}$. The following conclusions are given:
1. The domain of the function $f(x)$ is $(0, +\infty)$;
2. The function $f(x)$ is an odd function;
3. The minimum value of the function $f(x)$ is $-\lg 2$;
4. When $0 < x < 1$, the function $f(x)$ is increasing; when $x > 1$, the function $f(x)$ is decreasing.

Please write down the serial number(s) of all the conclusions you believe to be correct.

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