
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 mapping $f: A \to B$, where $A = [-1, 1]$ and $B = \mathbb{R}$, the mapping rule is $f: x \mapsto \log_{\frac{1}{2}}(2-x^2)$. For a real number $k \in B$, in order for $k$ to have a preimage in the set $A$, the range of values for $k$ is __________.

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