
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 $\frac{f(x_1) - f(x_2)}{x_1 - x_2} > 0$;  
③ $f'_{2015}(x) = xe^x + 2017e^x$;  
④ $f(x_1) + x_2 > f(x_2) + x_1$.  
The correct statement numbers are __________ (write down all numbers that satisfy the conditions of the problem).

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