
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 $n \in \mathbb{N}^*$.

(1) Find the general term formula for the sequence ${a_n}$.

(2) 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