
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 an ellipse $\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1$ ($a > b > 0$) whose left focus $F(-c, 0)$ is a quarter point of the major axis, and points $A$ and $B$ are respectively the left and right vertices of the ellipse. A line $l$ passing through point $F$ and not perpendicular to the y-axis intersects the ellipse at points $C$ and $D$. Let the slopes of lines $AD$ and $BC$ be $k_1$ and $k_2$ respectively.  
(1) When the sum of distances from point $D$ to the two foci is 4, and line $l$ is perpendicular to the x-axis, find the value of $k_1 : k_2$;  
(2) Find the value of $k_1 : k_2$.

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