
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
Given the circle \( \odot O: x^{2}+y^{2}=5 \) and the parabola \( C: y^{2}=2px \) (with \( p > 0 \)), they intersect at point \( A(x_{0}, 2) \). \( AB \) is a diameter of \( \odot O \). A line through point \( B \) intersects the parabola \( C \) at two points \( D \) and \( E \). Find the product of the slopes of the lines \( AD \) and \( AE \).

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