
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
The ratio of the distance from a moving point M on curve C to a fixed point F(1,0) and its distance to a fixed line x=3 is 1:$\sqrt{3}$.  
(I) Find the equation of curve C;  
(II) If a line l passes through point F(1,0) and intersects curve C at points A and B, when the area of triangle ΔABO is $\frac{2\sqrt{6}}{5}$, find the equation of line l.

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