
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 a mapping $f: A \rightarrow B$, where $A = B = \mathbb{R}$, and the rule of mapping $f$ is $f: x \mapsto y = x^2 - 2x - 1$. Determine the range of values for $k \in B$ such that there is no pre-image in set $A$.

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