
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 sequence $\{a\_n\}$ with the sum of its first $n$ terms denoted as $S\_n$. It is known that $a\_1= \frac {1}{2},S\_n=n^{2}a\_n-n(n-1),n=1,2,…$.

(1) Write out the recursive formula between $S\_n$ and $S\_{n-1}$ ($n\geqslant 2$), and find the values of $S\_2$ and $S\_3$;

(2) Find the expression of $S\_n$ in terms of $n$.

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