
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 a sequence $\{a\_n\}$ where all terms are positive, and it satisfies $a\_1=1$, $a \_{n+1} ^2 - a \_n ^2 = 2 (n \in \mathbb{N}^*)$.
(1) Find the general term formula for the sequence $\{a\_n\}$;
(2) Find the sum $S\_n$ of the first $n$ terms of the sequence $\{\frac{a\_n^2}{2^n}\}$.

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