
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 $f(x)=\ln\left(\frac{1-x}{1+x}\right)$. There are the following four propositions regarding this function:

1. The domain of $f(x)$ is $(-\infty, -1) \cup (1, +\infty)$;
2. $f(x)$ is an odd function;
3. $f(x)$ is an increasing function on its domain;
4. For any $x_1, x_2 \in (-1, 1)$, it holds that $f(x_1) + f(x_2) = f\left(\frac{x_1 + x_2}{1 + x_1x_2}\right)$.

Identify the true propositions from the above (write down the numbers of all true propositions).

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