
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 rectangular coordinate system $(xOy)$, the parametric equations of the curve $C_{1}$ are given by $\begin{cases}x=a\cos(\varnothing) \\ y=b\sin(\varnothing)\end{cases} (a > b > 0, \varnothing$ is a parameter), and the point $M(2, \sqrt{3} )$ on the curve $C_{1}$ corresponds to the parameter $\varnothing = \frac{π}{3} .$ Establish a polar coordinate system with $O$ as the pole and the positive semi-axis of $x$ as the polar axis. The curve $C_{2}$ is a circle with its center on the polar axis and passing through the pole. The ray $\theta= \frac{π}{4} $ intersects the curve $C_{2}$ at point $D\left( \sqrt{2}, \frac{π}{4}\right)$

(1) Find the Cartesian equation of curve $C_{1}$ and the polar equation of curve $C_{2}$;

(2) If $A\left({Ρ}_{1},θ\right) $ and $B\left({Ρ}_{2},θ+ \frac{π}{2}\right) $ are two points on curve $C_{1}$, find the value of $\frac{1}{{{ρ}_{1}}^{2}}+ \frac{1}{{{ρ}_{2}}^{2}}$.

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