
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 line l: y = kx + 3 and the circle C: x² + y² - 2y = 0 have no common points, AB is the diameter of circle C. If there exists a point P on line l such that $\overrightarrow {PA}\cdot \overrightarrow {PB}=1$, then the range of the slope k of line l is _____.

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