
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
Among the following four statements:  
1. Given a function $f(x+1)=x^2$, then $f(e)=(e-1)^2$.  
2. If the range of the function $f(x)$ is $(-2,2)$, then the range of the function $f(x+2)$ is $(-4,0)$.  
3. The graph of the function $y=2x$ ($x \in \mathbb{N}$) is a straight line.  
4. Given $f(x)$ and $g(x)$ are two functions defined on $\mathbb{R}$, for every $x, y \in \mathbb{R}$, the following relation holds: $f(x+y) + f(x-y) = 2f(x) \cdot g(y)$, and $f(0)=0$, but when $x \neq 0$, $f(x) \cdot g(x) \neq 0$; then the functions $f(x)$ and $g(x)$ are both odd functions.  
The incorrect statements are __________.

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