
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 there be a constant \(d\), so that among all chords \(\overline{AB}\) of the parabola \(y = x^2\) passing through \(D = (0,d),\) the sum
\[
s = \frac{1}{AD^2} + \frac{1}{BD^2}
\]
is a fixed constant. Find the constant \(s\).

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