
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 $(1+x)^n = 1 + a_1x + a_2x^2 + \ldots + a_nx^n$ ($n \in \mathbb{N}^*$), and $S_n = a_1 + 2a_2 + \ldots + na_n$ ($n \in \mathbb{N}^*$), then for $n \in \mathbb{N}^*$, the value of $$\sum\limits_{i=1}^{n}S_{i}$$ is \_\_\_\_\_\_.

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