
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 positive sequence \\(\{a_n\}\) with the first term being \\(1\\), and \\((a_n+a_{n+1})(a_{n+1}-a_n)+2a_n^2a_{n+1}^2=0, n \in \mathbb{N}^*\).  
\\((1)\\) Find the general formula for the sequence \\(\{a_n\}\);  
\\((2)\\) Let \\(b_n=a_na_{n+1}\), find the sum of the first \\(n\\) terms of the sequence \\(\{b_n^2\}\), denoted as \\(S_n\).

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