
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
A student's homework was accidentally stained with ink. After careful identification, the following two pieces of valid information were organized:

\\(①\\) Question: "In the Cartesian coordinate system \\(xOy\\), it is known that the left vertex of the ellipse \\(x^{2}+2y^{2}=1\\) is \\(A\\). Two rays passing through point \\(A\\) with the product of their slopes equal to \\(2\\) intersect the ellipse at points \\(B\\), \\(C……\\)"

\\(②\\) Solution: "Assume the slope of line \\(AB\\) is \\(k……\\) Point \\(B(\\dfrac{1\\mathrm{{-}}2k^{2}}{1{+}2k^{2}},\\dfrac{2k}{1{+}2k^{2}})\\), \\(D(-\\dfrac{5}{3},0)……\\)" Based on this, please write down the slope of line \\(CD\\) as \_\_\_\_\\(.(\\) expressed in terms of \\(k\\)\\()\\)

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