
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 $\{a_{n}+ \frac {1}{2}\}$ is a geometric sequence with first term $\frac {3}{2}$, and $a_{4}-a_{1}=39$.
(1) Find the general term formula for the sequence $\{a_{n}\}$;
(2) Let $f(x)=a_{n}x+a_{n-1}x^{2}+…+a_{1}x^{n}$. If $S_{n}=f'(1)$, find $S_{n}$.

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