
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\_n} where all terms are positive, it satisfies the conditions: a\_3 = 3a\_1, and a\_1, 4, 2a\_2 form a geometric sequence.
(1) Find the general term formula for the sequence {a\_n}.
(2) Let S\_n represent the sum of the first n terms of {a\_n}, and define b\_n = $\frac{1}{S\_n}$. Find the sum T\_n of the first n terms of the sequence {b\_n}.

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