
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 $\{a_n\}$ where $a_n^2 + 2a_n - n^2 + 2n = 0$ ($n \in \mathbb{N}^+$):

(Ⅰ) Find the general formula for the terms of the sequence $\{a_n\}$.

(Ⅱ) Calculate the sum of the first $n$ terms of the sequence $S_n$.

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