
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 the function $f(x)=a\_1+a\_2x+a\_3x^{2}+...+a\_n x^{n-1}$, where $f(0)=\frac{1}{2}$, and the sequence ${a\_n}$ satisfies $f(1)=n^2a\_n$ for all positive integers $n$. Determine the sum of the first $n$ terms of the sequence ${a\_n}$, denoted as $S\_n$, equals to \_\_\_\_\_\_.

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