
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 ${a_n}$ with its first $n$ terms sum $S_n$. The first two terms are $a_1=2$, $a_2=4$, and for $n\geq2$, $S_{n+1}+S_{n-1}=2S_n+2$ holds.
(1) Find the general term formula for the sequence ${a_n}$;
(2) If the sequence $\{ \frac {1}{a_{n} \,^{2}-1}+b_{n}\}$ is a geometric sequence with the first term and common ratio both being 2, find the sum of the first $n$ terms $T_n$ for the sequence ${b_n}$.

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