
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 $\begin{cases}x=a\cos \varphi \\ y=b\sin \varphi\end{cases} (a > b > 0,$ $\varphi$ is the parameter), and the point $M(2, \sqrt{3})$ on curve $C1$ corresponds to the parameter $\varphi= \frac{\pi}{3}$. Using $O$ as the pole and the positive half-axis of $x$ as the polar axis to establish a polar coordinate system, curve $C2$ is a circle with its center on the polar axis and passing through the pole. The ray $\theta= \frac{\pi}{4}$ intersects curve $C2$ at point $D(\sqrt{2}, \frac{\pi}{4})$.

$(1)$ Find the standard equation of curve $C1$ and the polar equation of curve $C2$;

$(2)$ If $A(\rho_{1},\theta),B(\rho_{2},\theta+ \frac{\pi}{2})$ are two points on curve $C1$, find the value of $\frac{1}{\rho_{1}^{2}+\rho_{2}^{2}}$.

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