
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
It is known that a function is defined on $\mathbb{R}$ and satisfies the following conditions: ① $f(4)=0$; ② the curve $y=f(x+1)$ is symmetric about the point $(-1,0)$; ③ when $x \in (-4,0)$, $$f(x)=\log_{2}\left( \frac{x}{e^{|x|}}+e^{x}-m+1\right)$$, if $y=f(x)$ has 5 zeros when $x \in [-4,4]$, then the range of the real number $m$ is \_\_\_\_\_\_.

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