
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
In the Cartesian coordinate system, a fixed point \( B \) is on the negative half of the y-axis. A variable line \( l \) passing through \( B \) intersects the ellipse \(\frac{x^2}{2} + y^2 = 1\) at points \( C \) and \( D \). The circle with diameter \( CD \) always passes through a fixed point \( A \) located above the x-axis. Determine the coordinates of \( A \).

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