
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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Given an arithmetic sequence {a<sub>n</sub>} with a common difference not equal to 0, a<sub>2</sub> = 5, and a<sub>1</sub>, a<sub>3</sub>, a<sub>11</sub> form a geometric sequence.
(I) Find the general term formula for the sequence {a<sub>n</sub>};
(II) If the sum of the first n terms S<sub>n</sub> of the sequence {b<sub>n</sub>} satisfies: $$S_{n}= \frac {1}{2}(1- \frac {1}{3^{n}})$$, find the sum of the first n terms T<sub>n</sub> of the sequence {a<sub>n</sub>b<sub>n</sub>}.

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