
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
$$
f(x)=
\begin{cases}
\log_{2}(1-x)+1 & , -1\leq x<k \\
x^{2}-2x+1 & , k\leq x\leq a
\end{cases}
$$
if there exists a real number $k$ such that the range of $f(x)$ is $[0,2]$, the range of the real number $a$ is \_\_\_\_\_\_.

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