
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 on a plane, the parametric equations of the ellipse $C$ are given by $\begin{cases} & x=2\cos \alpha , \ & y=\sqrt{3}\sin \alpha , \end{cases} (\alpha \text{ is the parameter})$ with the origin as a pole and the positive $x$-axis as the polar axis using the same unit length to establish the polar coordinate system.

(I) Convert the parametric equations of the ellipse $C$ to polar coordinate equations;

(II) Let $A$ and $B$ be two points on the ellipse $C$ such that $OA \perp OB$, find the value of $\frac{1}{|OA{{|}^{2}}}+\frac{1}{|OB{{|}^{2}}}$.

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