
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
Consider the following propositions:  
① The graph of the function $f(-x+2)$ is symmetric to the graph of $y=f(x-2)$ with respect to the y-axis.  
② If the function $f(x)=e^x$, then for any $x_1, x_2 \in \mathbb{R}$, it holds that $$f\left( \frac {x_{1}+x_{2}}{2}\right) \leq \frac {f(x_{1})+f(x_{2})}{2}$$  
③ If the function $f(x)=\log_a|x|$ ($a>0$, $a\neq1$) is monotonically increasing on $(0, +\infty)$, then $f(-2) > f(a+1)$  
④ If the function $f(x+2013)=x^2-2x-1$ ($x\in\mathbb{R}$), then the minimum value of the function is -2  
The correct proposition numbers are \_\_\_\_\_\_.

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