
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
In the arithmetic sequence $\{a_n\}$, $S_n$ denotes the sum of the first $n$ terms. It is known that $a_2=2$ and $S_5=15$. For the sequence $\{b_n\}$, we have $b_1=1$, and for any $n\in \mathbb{N}_+$, it satisfies $b_{n+1}=2b_n+1$.  
(i) Find the general formula for the terms in both sequences $\{a_n\}$ and $\{b_n\}$.  
(ii) Let $c_n = \frac{a_n}{b_n+1}$, find the sum of the first $n$ terms of the sequence $\{c_n\}$, denoted $T_n$.

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