
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 circle $C: x^2 + y^2 + 2kx + 2y + k^2 = 0$ ($k \in \mathbb{R}$) and a fixed point $P(1, -1)$, if there are two tangents that can be drawn from point P to circle C, then the range of values for $k$ is \_\_\_\_\_\_.

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