
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 the distance from point $M$ to point $F(2,0)$ is less than 4 times the distance from point $M$ to the line $x+6=0$:

(I) Find the equation of the trajectory $C$ of point $M$;

(II) If there exist two points $A$ and $B$ on the curve $C$ that are symmetric about the line $l: y = \frac{1}{4}x - 2$, find the equation of the line $AB$.

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