
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 $f(x)=xe^{x}$, let $f_{0}(x)=f'(x)$, $f_{1}(x)=f'_{0}(x)$, ..., $f_{n}(x)=f'_{n-1}(x)$ and $x_{2} > x_{1}$. For the following statements:

$(1)$ The function $f(x)$ has a tangent line parallel to the $x$-axis;   $(2)\dfrac{f(x_{1})-f(x_{2})}{x_{1}-x_{2}} > 0$;

$(3)f_{2016}(x)=xe^{x}+2017e^{x}$; $(4)f(x_{1})+x_{2} > f(x_{2})+x_{1}$.

Among these, the correct statement numbers are __________ (write down all the numbers that satisfy the condition of the problem).

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