
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 all terms of the geometric sequence $\{an\}$ are positive numbers, the first three terms are $a-2$, $4$, and $2a$, respectively. Denote the sum of the first $n$ terms as $Sn$. Let $bn=(2n-1)Sn$, find the sum of the first $n$ terms of the sequence $\{bn\}$, denoted as $Tn$.

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