
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 $\{a_n\}$, where $a_1=1$, $a_2=\sqrt{2}$, and $2a_n^2=a_{n-1}^2+a_{n+1}^2$ ($n\geqslant 2$), let $b_n=\frac{1}{a_n+a_{n+1}}$. Denote the sum of the first $n$ terms of the sequence $\{b_n\}$ as $S_n$. Calculate the value of $S_{15}$.

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