
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 $f(x)=\begin{cases} \log_{ \frac{1}{2}}(-x+1)-1, & x\in[-1,k], \\ -2|x-1|, & x\in(k,a], \end{cases}$ if there exists a real number $k$ such that the range of this function is $[-2,0]$, then the range of the real number $a$ is ______.

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