
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 the ellipse \\(C: \dfrac{x^2}{a^2} + \dfrac{y^2}{b^2} = 1, (a > b > 0)\\) have an eccentricity of \\(\dfrac{2\sqrt{2}}{3}\\), and it is inscribed in the circle \\(x^2 + y^2 = 9\\).

\\((1)\\) Find the equation of ellipse \\(C\\).

\\((2)\\) A line \\(l\\) (not perpendicular to the x-axis) passing through point \\(Q(1,0)\\) intersects the ellipse at points \\(M\\) and \\(N\\), and intersects the y-axis at point \\(R\\). If \\(\overrightarrow{RM} = \lambda \overrightarrow{MQ}\\) and \\(\overrightarrow{RN} = \mu \overrightarrow{NQ}\\), determine whether \\(\lambda + \mu\\) is a constant, and explain why.

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