
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
Let point \\(A\\) be a point on the ellipse \\(E\\): \\( \dfrac {x^{2}}{a^{2}}+ \dfrac {y^{2}}{b^{2}}=1(a > b > 0)\\), and let \\(F_{1}\\) and \\(F_{2}\\) be the left and right foci of the ellipse \\(E\\), respectively. Given that \\(\angle AF_{1}F_{2}=15^{\circ}\\) and \\(\angle AF_{2}F_{1}=75^{\circ}\\), and \\(|F_{1}F_{2}|=2 \sqrt {6}\\):
\\((1)\\) Find the equation of the ellipse \\(E\\);
\\((2)\\) If point \\(M( \dfrac {3}{2}, \dfrac {3}{2})\\) is a point on the ellipse \\(E\\), and \\(N\\) is the symmetric point of \\(M\\) with respect to the origin \\(O\\), and a line passing through \\(M\\) (but not through the origin \\(O)\\) intersects the ellipse \\(E\\) at another point \\(Q\\), find the maximum area of \\(\triangle MQN\\).

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