
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 distance from point M to line l: x = -1 is equal to its distance from fixed point F(1, 0).
(1) Find the equation of the trajectory C of point M;
(2) Let line l1 passing through point F with a slope of k intersect curve C at two points A and B, and |AB| = 6, find the equation of l1.

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