
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 sequence $\{a_n\}$ have a sum of the first $n$ terms denoted by $S_n$, and $a_1=1$, $a_{n+1}=2S_n+1$. The sequence $\{b_n\}$ satisfies $a_1=b_1$, and the point $P(b_n,b_{n+1})$ lies on the line $x-y+2=0$, where $n\in\mathbb{N}^*$.  
$(1)$ Find the general formula for the sequences $\{a_n\}$ and $\{b_n\}$.  
$(2)$ Let $c_n= \frac {b_n}{a_n}$, find the sum of the first $n$ terms of the sequence $\{c_n\}$, denoted by $T_n$.

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