
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
Let the set $A=\{x|0\leqslant x < 1\}$, $B=\{x|1\leqslant x\leqslant 2\}$, and the function $f(x)= \begin{cases} 2^{x}, & (x\in A) \\ 4-2x, & (x\in B) \end{cases}$. If $x_{0}\in A$ and $f[f(x_{0})]\in A$, then the range of $x_{0}$ is \_\_\_\_\_\_.

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