
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 points $M(-1,0)$ and $N(1,0)$, the distance from any point on curve $E$ to point $M$ is $\sqrt{3}$ times the distance to point $N$.

(I) Find the equation of curve $E$.

(II) Given that $m \neq 0$, let line $l_{1}: x - my - 1 = 0$ intersect curve $E$ at points $A$ and $C$, and line $l_{2}: mx + y - m = 0$ intersect curve $E$ at points $B$ and $D$. If the slope of $CD$ is $-1$, find the equation of line $CD$.

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