
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
In the arithmetic sequence $\{a_n\}$, the common difference $d \neq 0$, $a_1 = 3$, and $a_1$, $a_4$, $a_{13}$ form a geometric sequence.  
(I) Find $a_n$;  
(II) Let the sum of the first $n$ terms of $\{a_n\}$ be $S_n$, find: $$\frac {1}{S_{1}}+ \frac {1}{S_{2}}+…+ \frac {1}{S_{n}}$$.

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