
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 $S\_n=2n^2$, and ${\_}{b\_n}$ is a geometric sequence with $a\_1=b\_1$ and $b\_2(a\_2-a\_1)=b\_1$.

1. Find the general term formulas for the sequences ${\_}{a\_n}$ and ${\_}{b\_n}$;
2. Let $c\_n= \dfrac{a\_n}{b\_n}$, 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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