
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 a geometric sequence ${ a_{n} }$ is $S_{n}$, where $S_{n}=2a_{n}-2$, and ${ b_{n} }$ is an arithmetic sequence with $b_{3}=a_{2}$ and $b_{2}+b_{6}=10$.

1. Find the general term formulas for the sequences ${ a_{n} }$ and ${ b_{n} }$.
2. Find the sum of the first $n$ terms, $T_{n}$, of the sequence ${ a_{n}(2b_{n}-3) }$.

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