
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 function $f(x)=\begin{cases} kx+2, & x\geqslant 0\\ (\frac{1}{2})^{x}, & x < 0 \end{cases}$, if the function $y=f[f(x)]-\frac{3}{2}$ has exactly $3$ zero points, then the range of the real number $k$ is \_\_\_\_\_\_\_\_.

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