
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 $(E)$ with its center at the origin of the coordinate system, one endpoint of its major axis is the focus of the parabola $y^{2}=4 \sqrt {5}x$. The eccentricity of ellipse $(E)$ is $\dfrac { \sqrt {5}}{5}$.
(1) Find the equation of ellipse $(E)$;
(2) A tangent line passing through point $C(-1,0)$ intersects ellipse $(E)$ at points $A$ and $B$. If the $x$-coordinate of the midpoint of segment $AB$ is $-\dfrac {1}{2}$, find the equation of line $AB$.

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