
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
Let the function be $f(x)=x|x|+bx+c$. Consider the following four statements:  
1. When $c=0$, $f(-x)=-f(x)$ holds;  
2. When $b=0$ and $c > 0$, the equation $f(x)=0$ has only one real root;  
3. The graph of the function $y=f(x)$ is symmetric about the point $(0,c)$;  
4. When $x > 0$, the function $f(x)=x|x|+bx+c$ has a minimum value of $c- \frac {b^{2}}{2}$.  

Among these statements, the correct ones are \_\_\_\_\_\_.

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