
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 an arithmetic sequence {a<sub>n</sub>} where the sum of the first n terms is S, the common ratio q > 1, and a<sub>2</sub> + 1 is the arithmetic mean of a<sub>1</sub> and a<sub>3</sub>, and S<sub>3</sub> = 14.
(I) Find the general term formula for the sequence {a<sub>n</sub>}.
(II) Let b<sub>n</sub> = a<sub>n</sub> • log<sub>2</sub>a<sub>n</sub>, 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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