
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
Let the sum of the first $n$ terms of an arithmetic sequence $\{a_n\}$ be $S_n$, and it is given that $S_4=4S_2$, $a_{2n}=2a_n+1$.

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

(Ⅱ) Let the sequence $\{b_n\}$ satisfy $\frac{b_1}{a_1}+\frac{b_2}{a_2}+\cdots+\frac{b_n}{a_n}=1-\frac{1}{2^n}$, $(n\in\mathbb{N}^*)$, find the sum of the first $n$ terms of $\{b_n\}$, $T_n$.

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