
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 $$E: \frac{x^2}{a^2} + \frac{y^2}{b^2} = 1 (a > b > 0)$$ with a minor axis length of 2 and an eccentricity of $$\frac{2\sqrt{5}}{5}$$, and a parabola $$G: y^2 = 2px (p > 0)$$ whose focus $F$ coincides with the right focus of the ellipse $E$. If a line $l$ with slope $k$ passes through the focus $F$ of the parabola $G$ and intersects the ellipse $E$ at points $A$ and $B$, and intersects the parabola $G$ at points $C$ and $D$.
(Ⅰ) Find the equations of the ellipse $E$ and the parabola $G$;
(Ⅱ) Does there exist a real number $\lambda$ such that $$\frac{1}{|AB|} + \frac{\lambda}{|CD|}$$ is constant? If it exists, find the value of $\lambda$; if not, explain why.

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