
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 $S_n = \frac{n^2 + n}{2}, n \in \mathbb{N}^*$.

(1) Find the general term formula for $\{a_n\}$;

(2) Let $\{b_n\} = 2^{a_n} + (-1)^n a_n$, find the sum of the first $2n$ terms of $\{b_n\}$.

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