
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 sequence $\{a\_n\}$: $\frac{1}{2}$, $\frac{1}{3}+\frac{2}{3}$, $\frac{1}{4}+\frac{2}{4}+\frac{3}{4}$, $\frac{1}{5}+\frac{2}{5}+\frac{3}{5}+\frac{4}{5}$, ..., find the sum of the first $n$ terms of the sequence $\{b\_n=\frac{1}{a\_na\_{n+1}}\}$.

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