
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
In the Cartesian coordinate system $xOy$, the parametric equation of curve $C_{1}$ is $\begin{cases} x=a\cos \phi \\ y=b\sin \phi \end{cases}$ ($a > b > 0$, $\phi$ is the parameter), and the point $M(2, \sqrt {3})$ on curve $C_{1}$ corresponds to the parameter $\phi= \dfrac {\pi}{3}$. Taking $O$ as the pole and the positive half-axis of $x$ as the polar axis, we establish a polar coordinate system. Curve $C_{2}$ is a circle with its center on the polar axis and passing through the pole. The ray $\theta= \dfrac {\pi}{4}$ intersects curve $C_{2}$ at point $D(\sqrt {2}, \dfrac {\pi}{4})$.  
$(1)$ Find the standard equation of curve $C_{1}$ and the polar equation of curve $C_{2}$;  
$(2)$ If $A(\rho_{1},\theta)$ and $B(\rho_{2},\theta+ \dfrac {\pi}{2})$ are two points on curve $C_{1}$, find the value of $ \dfrac {1}{\rho _{1}^{2}}+ \dfrac {1}{\rho _{2}^{2}}$.

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