
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 sequence $\{a\_n\}$ satisfies $a\_1=1$, and $a_{n+1}-a_{n}=2^{n}$ for all $n \in \mathbb{N}^*$.

(I) Find the general term formula for the sequence $\{a\_n\}$;
(II) If $\{b\_n\} = n \cdot a\_n$, find the sum of the first $n$ terms, denoted as $S\_n$, for the sequence $\{b\_n\}$.

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