
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 that the polar coordinate equation of curve $C$ is ${{\rho }^{2}}=\frac{9}{{{\cos }^{2}}\theta +9{{\sin }^{2}}\theta }$, establish a rectangular coordinate system with the pole as the origin and the positive semi-axis of the polar axis as the $x$-axis.

(1) Find the Cartesian equation of curve $C$;

(2) Let $A$ and $B$ be two points on curve $C$. If $OA\perp OB$, 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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