
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
The sequence $\{a\_n\}$ satisfies $a\_1=1$, $\sqrt{\frac{1}{a\_n^2} + 2} = \frac{1}{a\_{n+1}}(n \in \mathbb{N}^+)$. Let $b\_n = a\_n^2$, then the sum of the first $n$ terms of the sequence $\{b\_n b\_{n+1}\}$, denoted as $S\_n$, is $\_\_\_\_\_\_\_\_\_$.

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