
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 that the function $f(x) (x \in \mathbb{R})$ satisfies $f(-x) = -f(x) = f(4-x)$, when $x \in (0, 2)$, $f(x) = \ln(x^2 - x + b)$. If the function $f(x)$ has 5 zero points in the interval $[-2, 2]$, then the range of the real number $b$ is _____.

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