
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 that the sum of the first $n$ terms of the sequence ${a_n}$ is $S_n$, and $4S_n=(2n-1)a_{n+1}+1$, with $a_1=1$.

1. Find the general term formula for the sequence ${a_n}$.
2. If the sequence ${b_n}$ satisfies $\frac{b_n}{a_n}=\sqrt{2}^{1+a_n}$, find the sum of the first $n$ terms of the sequence ${b_n}$, denoted as $T_n$.

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