
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
The domain of the function $f(x)$ is $D$. If it satisfies (1) $f(x)$ is a monotonic function within $D$, and (2) there exists an interval $[a,b] \subseteq D$ such that the range of $f(x)$ on $[a,b]$ is $[-b,-a]$, then $y = f(x)$ is called a symmetric function. Given that $f(x) = \sqrt{2 - x} - k$ is a symmetric function, the range of values for $k$ is ______.

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