
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
Let S<sub>n</sub> be the sum of the first n terms of a geometric sequence {a<sub>n</sub>}. Given that a<sub>1</sub>, a<sub>2</sub>, and S<sub>2</sub> form an arithmetic sequence, and S<sub>3</sub> = 42.
(1) Find the general term formula a<sub>n</sub> for the sequence {a<sub>n</sub>};
(2) Let $$b_{n}= \frac {na_{n}}{2^{n}}$$. If $$c_{n}= \frac {1}{b_{n}b_{n+1}}$$, find the sum of the first n terms T<sub>n</sub> for the sequence {c<sub>n</sub>}.

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