
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 $O: x^2 + y^2 = 1$. If there always exists a point $P$ on the line $y = \sqrt{k}x + 2$ such that the two tangents from $P$ to the circle $O$ are perpendicular to each other, then the minimum value of the real number $k$ is \_\_\_\_\_.

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