
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 that the sequence $\{\frac{{a}_{n}}{n}\}$ is an arithmetic sequence, $a_{3}-3a_{1}=6$, and $a_{2}=6$.  
$(1)$ Find $a_{n}$;  
$(2)$ Let $S_{n}$ be the sum of the first $n$ terms of the sequence $\{\frac{1}{{a}_{n}}\}$, find $S_{n}$.

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