
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]


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Let the sequence $\{a_n\}$ be an arithmetic sequence, and the sum of the first $n$ terms of the sequence $\{b_n\}$, denoted as $S_n$, satisfies $S_n=1-b_n$ $(n\in\mathbb{N}^+)$, and $a_2-1= \frac {1}{b_1}$, $a_5= \frac {1}{b_3}+1$.  
(I) Find the general formula for sequences $\{a_n\}$ and $\{b_n\}$.  
(II) Let $T_n$ be the sum of the first $n$ terms of the sequence $\{a_n\cdot b_n\}$, find $T_n$.

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