
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 the functions $f(x)=\begin{cases} 2^{x-2} - 1, & x \geq 0 \\ x + 2, & x < 0 \end{cases}$ and $g(x)=\begin{cases} x^2 - 2x - 1, & x \geq 0 \\ \frac{1}{x}, & x < 0 \end{cases}$, find the sum of all zero points of the function $f[g(x)]$.

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