
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 sequence $\{a_n\}$ with the sum of its first $n$ terms $S_n=n^2-n$ ($n\in N^*$). The positive geometric sequence $\{b_n\}$ has its first term $b_1=1$, and $3a_2$ is the arithmetic mean of $b_2$ and $b_3$.  
(I) Find the general formula for the sequences $\{a_n\}$ and $\{b_n\}$.  
(II) If $c_n= \frac {a_n}{b_n}$, find the sum of the first $n$ terms $T_n$ of the sequence $\{c_n\}$.

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