
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 $(x+1)^{n}=a_{0}+a_{1}(x-1)+a_{2}(x-1)^{2}+a_{3}(x-1)^{3}+…+a_{n}(x-1)^{n}$, where $n\in\mathbb{N}^{*}$
(1) Find $a_{0}$ and $S_{n}=a_{1}+2a_{2}+3a_{3}+…+na_{n}$;
(2) Compare $S_{n}$ with $n^{3}$ and explain the reason.

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