
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 an arithmetic sequence $\{a\_n\}$ with the sum of its first $n$ terms denoted as $S\_n$, it is known that $S\_n - a\_n = n^2 - n$, where $n \in \mathbb{N}^+$.

1. Find the general term formula for the sequence $\{a\_n\}$.
2. Suppose another sequence $\{b\_n\}$ satisfies $b\_n = \begin{cases} \frac{1}{\sqrt{n-1} + \sqrt{n+1}}, & \text{if } n=2k-1 \\ \frac{1}{a\_{\frac{n}{2}}a\_{\frac{n}{2}+1}}, & \text{if } n=2k \end{cases}$, where $k \in \mathbb{N}^+$. Let $T\_n$ denote the sum of the first $n$ terms of $\{b\_n\}$. Compute $T\_{2016}$.

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