
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 an arithmetic sequence $\{a\_n\}$ with a non-zero common difference, the sum of its first 4 terms is 20, and $a\_1$, $a\_2$, $a\_4$ form a geometric sequence.
(I) Find the general term formula for the sequence $\{a\_n\}$.
(II) Let $b\_n = n \cdot 2^{a\_n}$, find the sum $S\_n$ of the first $n$ terms of the sequence $\{b\_n\}$.

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