
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 any point $P$ on curve $E$ has a constant sum of distances to two fixed points $F_{1}(-\sqrt{3},0)$ and $F_{2}(\sqrt{3},0)$ equal to 4,  
(1) find the equation of curve $E$;  
(2) suppose a line $l$ passing through $(0, -2)$ intersects curve $E$ at points $C$ and $D$, and $\overrightarrow{OC} \cdot \overrightarrow{OD} = 0$ (where $O$ is the origin), find the equation of line $l$.

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