
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 two fixed points on the plane, \\(A(-2,0)\\) and \\(B(2,0)\\), and a moving point \\(T\\) satisfying \\(|TA|+|TB|=2 \sqrt {6}\\).
\\((\\)I\\()\\) Find the equation of the trajectory \\(E\\) of point \\(T\\);
\\((\\)II\\()\\) A line passing through point \\(B\\) and having the equation \\(y=k(x-2)\\) intersects the trajectory \\(E\\) at points \\(P\\) and \\(Q\\) \\((k\neq 0)\\). If \\(PQ\\)'s midpoint is \\(N\\) and \\(O\\) is the origin, the line \\(ON\\) intersects the line \\(x=3\\) at point \\(M\\). Find the maximum value of \\( \dfrac {|PQ|}{|MB|}\\).

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