
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 ellipse $$\frac{x^{2}}{a^{2}} + \frac{y^{2}}{b^{2}} = 1$$ with its left vertex at A and upper vertex at B, a line is drawn perpendicular to the x-axis passing through the right focus of the ellipse C, intersecting line AB at point D. If the slope of line OD is k times the slope of line AB, where O is the origin and k > 5, determine the range of the eccentricity e of ellipse C.

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