
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
Given the parabola $y=n(n+1)x^2-(2n+1)x+1$, where $n$ is a natural number, calculate the value of $|A_nB_n|+|A_2B_2|+...+|A_{2017}B_{2017}|$.

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