
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 lines $l_{1}$: $\rho\sin(\theta-\frac{\pi}{3})=\sqrt{3}$ and $l_{2}$: $\begin{cases} x=-t \\ y=\sqrt{3}t \end{cases}$ (where $t$ is a parameter), find the polar coordinates of the intersection point $P$ of $l_{1}$ and $l_{2}$. Additionally, three points $A$, $B$, and $C$ lie on the ellipse $\frac{x^{2}}{4}+y^{2}=1$, with $O$ being the coordinate origin. If $\angle{AOB}=\angle{BOC}=\angle{COA}=120^{\circ}$, find the value of $\frac{1}{|OA|^{2}}+\frac{1}{|OB|^{2}}+\frac{1}{|OC|^{2}}$.

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