
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: kx - y - 2k + 1 = 0 intersects with the ellipse $$\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1$$ (a > b > 0) at points A and B, and intersects with the circle C₂: (x - 2)² + (y - 1)² = 1 at points C and D. If there exists $$k \in [-2, -1]$$ such that $$\overrightarrow{AC} = \overrightarrow{DB}$$, determine the range of the eccentricity of the ellipse $$\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1$$

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