
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 a sequence ${a_n}$ with the sum of its first $n$ terms denoted as $S_n$. For any $n \in \mathbb{N}^*$, it is known that $2a_n = S_n + n$.

1. Find the general formula for the terms of the sequence ${a_n}$.
2. Let $f(n) = n^2$ ($n \in \mathbb{N}^*$). Compare the magnitude of $S_n$ and $f(n)$ and provide an explanation.

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