
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
A sequence $\{a\_n\}$ satisfies $a\_1=1$, $\sqrt{\frac{1}{a\_n^2}+2}=\frac{1}{a\_{n+1}} (n\in\mathbb{N}^*)$, and $b\_n=\frac{1}{a\_n^2\cdot 2^n}$. Determine the sum of the first $n$ terms of the sequence $\{b\_n\}$, denoted as $S\_n=$ \_\_\_\_\_\_.

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