
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
In the arithmetic sequence {a<sub>n</sub>}, the common difference d > 0, and a<sub>2</sub> + a<sub>6</sub> = 8, a<sub>3</sub>a<sub>5</sub> = 12.
(1) Find the general term formula for the sequence {a<sub>n</sub>};
(2) Let $$b_{n}=(a_{n}+4)\cdot 2^{n}$$, find the sum of the first n terms T<sub>n</sub> for the sequence {b<sub>n</sub>}.

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