
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 its first $n$ terms sum $S\_n$, and $a\_1=1$, $a_{n+1}=3S\_n (n\in\mathbb{N}^*)$.

1. Find the general term formula for the sequence $\{a\_n\}$.
2. Let $b\_n=n\cdot a\_n$, find the sum of the first $n$ terms of the sequence $\{b\_n\}$.

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