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

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