
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 points $A_{n}, B_{n}$. Determine the value of $\left|A_{1} B_{1}\right| + \left|A_{2} B_{2}\right| + \cdots + \left|A_{1992} B_{1992}\right|$.

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