
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 \( c \), so that among all chords \( \overline{AB} \) of the parabola \( y = 4x^2 \) passing through \( C = (1,c), \)
\[ t = \frac{1}{AC^2} + \frac{1}{BC^2} \] is a fixed constant. Find the constant \( t \).

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