
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 $\left\{ a_n \right\}$, the sum of the first $n$ terms, denoted as $S_n$, satisfies $S_n=2a_n-2$.

(Ⅰ) Find the general formula for the sequence $\left\{ a_n \right\}$;

(Ⅱ) Find the sum of the first $n$ terms, denoted as $T_n$, for the sequence $\left\{ (2n-1)\cdot a_n \right\}$.

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