
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 $\{b_n\}$ with the sum of its first $n$ terms $B_n= \frac {3n^{2}-n}{2}$.  
(I) Find the general formula for the sequence $\{b_n\}$.  
(II) Let the sequence $\{a_n\}$ have the general term $a_n=[b_n+(-1)^{n}]\cdot 2^{n}$, find the sum of the first $n$ terms of the sequence $\{a_n\}$, denoted as $T_n$.

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