
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 sequences $\{a\_n\}$ and $\{b\_n\}$, if $b\_1=0$, $a\_n= \frac{1}{n(n+1)}$, and $b\_n = b\_{n-1} + a\_{n-1}$ when $n \geqslant 2$, find the value of $b\_{2017}$.

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