
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 point \\(F(0,1)\\) and line \\(l\\): \\(y=-1\\), if a moving point \\(M\\) is equidistant from point \\(F\\) and line \\(l\\),

\\((\\)I\\()\\) find the equation of the trajectory \\(E\\) of point \\(M\\);

\\((\\)II\\()\\) line \\({{l}\_{1}}\\) passes through point \\(F\\) and intersects curve \\(E\\) at two distinct points \\(A\\) and \\(B\\). If \\(|AB|=12\\), find the equation of line \\({{l}\_{1}}\\).

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