
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
For the following statements:
① The graph of the function $y=a^{x+2}$ ($x \in \mathbb{R}$) can be obtained by translating the graph of the function $y=a^x$ ($a>0$ and $a \neq 1$);
② The graph of the function $y=2^x$ and the graph of the function $y=\log_{2}x$ are symmetric about the y-axis;
③ The solution set of the equation $\log_{5}(2x+1)=\log_{5}(x^2-2)$ is $\{-1,3\}$;
④ The function $y=\ln(1+x)-\ln(1-x)$ is an odd function.
Among these statements, the correct ones are ______ (Fill in the numbers of all correct statements).

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