
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 the sequence $\{a_{n}\}$, where $a_{1}=2$, and for any positive integer $n$, $a_{n+1}-a_{n}=2^{n}$.
(I) Find the general term formula for the sequence $\{a_{n}\}$.
(II) Let $b_{n}= \frac{4n^{2}}{(\log_{\sqrt{2}}a_{n})^{2}-1}$, find the sum of the first $n$ terms, $T_{n}$, of the sequence $\{b_{n}\}$.

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