
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 the function $y=f(x)$ ($x \in \mathbb{R}$) satisfies $f(x)=2x+1$, and for the sequence $\{a_n\}$, $a_1=1$, $a_{n+1}=f(a_n)-1$ ($n \in \mathbb{N}^*$), the sequence $\{b_n\}$ is an arithmetic sequence with the first term $b_1=1$ and common difference $2$.  
(1) Find the general formula for the sequences $\{a_n\}$ and $\{b_n\}$.  
(2) Let $c_n= \frac {b_n}{a_n}$ ($n \in \mathbb{N}^*$), find the sum of the first $n$ terms of $\{c_n\}$, denoted as $T_n$.

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