
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 a non-zero common difference arithmetic sequence {a<sub>n</sub>} with the sum of the first n terms denoted as S<sub>n</sub>, if S<sub>6</sub>=60 and a<sub>6</sub> is the geometric mean of a<sub>1</sub> and a<sub>21</sub>, find:

(I) a<sub>n</sub> and S<sub>n</sub>.
(II) If sequence {b<sub>n</sub>} satisfies b<sub>n+1</sub>-b<sub>n</sub>=a<sub>n</sub> and b<sub>1</sub>=3, find the sum of the first n terms, T<sub>n</sub>, of the sequence {$$\frac {1}{b_{n}}$$} (n∈N*).

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