
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 $\{a_n\}$ whose sum of the first $n$ terms is $S_n$, and $S_n=2a_n-3$, where $n\in\mathbb{N}^*$. 

(1) Find the general formula for the sequence $\{a_n\}$.

(2) Let $b_n=(n-1)a_n$, and the sum of the first $n$ terms of the sequence $\{b_n\}$ is $T_n$.

   (i) Find $T_n$.
   
   (ii) If the inequality $T_n > ka_n+16n-26$ holds for all $n\in\mathbb{N}^*$, find the range of the real number $k$.

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