
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 $\{a\_n\}$ with the sum of its first $n$ terms $S\_n=\frac{n^2+n}{2}$, where $n \in \mathbb{N}^*$.
(I) Find the general formula for the sequence $\{a\_n\}$.
(II) Let $b\_n = 2^{a\_n} + (-1)^n a\_n$. Find the sum of the first $2n$ terms of the sequence $\{b\_n\}$.

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