
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
A sequence ${a_n}$ has a sum of the first $n$ terms given by $S_n=2^{n+1}-2$. Another sequence ${b_n}$ is an arithmetic sequence with first term $a_1$ and common difference $d (d\neq 0)$. Additionally, $b_1$, $b_3$, and $b_{11}$ form a geometric sequence.

1. Find the general term formulae for the sequences ${a_n}$ and ${b_n}$.
2. Let $c_n=\frac{b_n}{a_n}$. Find the sum of the first $n$ terms of the sequence ${c_n}$, denoted as $T_n$.

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