
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
In data processing, we often round off the obtained data. For any real number $x$, define a rounding function $f(x)$ precise to the integer part, i.e., if $n-0.5 \leqslant x < n+0.5$ ($n \in \mathbf{Z}$), then $f(x) = n$. For example, $f(3.49) = 3$, $f(-1.2) = -1$, $f(-2.5) = -2$, etc. Consider the following statements about the function $f(x)$:
1. $f(x)$ is an odd function;
2. $f(x)$ is an increasing function;
3. For any $m \in \mathbf{Z}$, $f(x+m) = f(x) + m$;
4. For any $x, y \in \mathbf{R}$, $f(x+y) \geqslant f(x) + f(y)$;
5. For any $x, y \in \mathbf{R}$, $f(x+y) \leqslant f(x) + f(y)$.

Which of the above statements are correct? (Enter the serial number).

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