
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 a moving point $M(x,y)$ at a distance $d_{1}$ from the point $F(2,0)$, and at a distance $d_{2}$ from the line $x=3$, with $\frac {d_{1}}{d_{2}}= \frac { \sqrt {6}}{3}$.  
$(1)$ Find the equation of the trajectory $C$ of the moving point $M(x,y)$.  
$(2)$ Draw a line $l$: $y=k(x-2) (k\neq 0)$ through point $F$ that intersects curve $C$ at points $P$ and $Q$. If the area of $\triangle OPQ$ is $S_{\triangle OPQ}= \sqrt {3}$ (where $O$ is the origin of the coordinate system), find the equation of line $l$.

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