
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]


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Let \\(O\\) be the origin of coordinates. It is known that the eccentricity of the ellipse \\(C_{1}\\): \\(\dfrac{x^{2}}{a^{2}} + \dfrac{y^{2}}{b^{2}} = 1 (a > b > 0)\\) is \\(\dfrac{\sqrt{3}}{2}\\), and the equation of the directrix of the parabola \\(C_{2}\\): \\(x^{2} = -ay\\) is \\(y = \dfrac{1}{2}\\).  
(Ⅰ) Find the equations of the ellipse \\(C_{1}\\) and the parabola \\(C_{2}\\);  
(Ⅱ) Suppose a line \\(l\\) passes through the fixed point \\(M(0,2)\\) and intersects the ellipse \\(C_{1}\\) at two distinct points \\(P\\) and \\(Q\\). If \\(O\\) lies on the circle with diameter \\(PQ\\), find the slope of line \\(l\\).

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