
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
Known is an ellipse $\frac{x^2}{3} + y^2 = 1$. Given the fixed point E(-1, 0), consider the line $y=kx+2$ ($k \neq 0$) which intersects the ellipse at points C and D. Is there a value of $k$ for which the circle with CD as its diameter passes through point E? Please explain your reasoning.

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