
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 $f(x) = x + \sin x$, there are the following five statements:
1. $f(x)$ is an odd function;
2. $f(x)$ is monotonic on $(-\infty, +\infty)$;
3. When $x > 0$, $f(x) > 0$; when $x < 0$, $f(x) < 0$;
4. $f(x)$ is a periodic function;
5. The graph of $f(x)$ is symmetric about the line $y = -x$.

Among these statements, the correct ones are. (Fill in the sequence numbers)

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