
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
There exists a constant $d$ such that, for all chords $\overline{AB}$ of the parabola $y = x^2 + 1$ passing through $C = (0,d),$ the value of
\[ s = \frac{1}{AC^2} + \frac{1}{BC^2} \]
is a fixed constant. Find the constant $s$.

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