
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
Given the function $f(x)=x|x-a|$, where $a\in\mathbb{R}$. The following statements are made about the function $f(x)$:

1. Regardless of the real number $a$ taken, the graph of the function $f(x)$ passes through the origin;
2. If $f(x)$ is an odd function, then $a=0$;
3. When $a > 2$, the analytical expression of function $f(x)$ on $(-\infty,2]$ is $f(x)=-x^{2}+ax$;
4. When $a=1$, the function $f(x)$ has a maximum value of $\frac{1}{4}$;
5. When $a=2$, if the equation $f(x)-m=0(m\in\mathbb{R})$ has three roots, then $0 < m < 1$.

The sequence numbers of all correct statements are \_\_\_\_\_\_\_\_.

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