
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
For each natural number \( n \), the parabola \( y = (n^2 + n)x^2 - (2n + 1)x + 1 \) intersects the \( x \)-axis at two points \( A_n \) and \( B_n \). Find the value of \( |A_1 B_1| + |A_2 B_2| + \cdots + |A_{1992} B_{1992}| \).

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