
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 an ellipse \\(C\\): \\(\dfrac {x^{2}}{a^{2}}+ \dfrac {y^{2}}{b^{2}}=1\\) with \\(a > b > 0\\), its left and right foci are respectively \\(F_1\\) and \\(F_2\\), and the symmetric point \\(M\\) of \\(F_2\\) with respect to the line \\(x-y+a=0\\) lies on the line \\(3x+2y=0\\).
\\((1)\\) Find the eccentricity of the ellipse;
\\((2)\\) If the major axis of ellipse \\(C\\) is 4 and a line \\(l\\) with a slope of \\(\dfrac {1}{2}\\) intersects the ellipse at points \\(A\\) and \\(B\\), is there a fixed point \\(P\\) such that the sum of the slopes of \\(PA\\) and \\(PB\\) is a constant value? If yes, find the coordinates of all such points \\(P\\); if no, explain why.

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