
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 $C_{1}$: $ \dfrac {x^{2}}{a^{2}}+ \dfrac {y^{2}}{b^{2}}=1(a > b > 0)$ with eccentricity $e$, and the hyperbola $E$: $x^{2}-y^{2}=2$ share common foci, and it is tangent to the line $y=2 \sqrt {3}$. Let the parabola $C_{2}$ be $x^{2}=4ey$. Find:  
$(1)$ The standard equations of the ellipse $C_{1}$ and the parabola $C_{2}$;  
$(2)$ The line $l$ is tangent to the parabola $C_{2}$ at point $D(x_{0}, \dfrac {x_{0}^{2}}{4e})(x_{0} < 0)$, $l$ intersects the ellipse $C_{1}$ at points $A$ and $B$, and intersects the $y$-axis at point $M(0,y_{M})$. If $ \overrightarrow{AM}=\lambda \overrightarrow{AD}$ and $ \overrightarrow{BM}=\mu \overrightarrow{BD}$, when $- \dfrac {1}{2}\leqslant y_{M} < 0$, find the range of $\lambda+\mu$.

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