
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 set $A=[0,1)$ and $B=[1,2]$, and the function $f(x)= \begin{cases} x+ \frac {1}{2},x∈A \\ 2(1-x),x∈B\\end{cases}$, if $x_{0}∈A$, and $f[f(x_{0})]∈A$, then the value of $x_{0}$ is _____.

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