
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 that the terms of the infinite sequence $\{a\_n\}$ are all positive integers, and $S\_n$ represents the sum of the first $n$ terms of the sequence.
(I) If the sequence is an arithmetic sequence, and for any positive integer $n$, $S_{n^2} = (S_n)^2$ holds, find the general term formula of the sequence.
(II) For any positive integer $n$, a number of terms are selected from the set $\{a_1, a_2, \ldots, a_n\}$ without repetition. After addition and subtraction operations, the absolute values of the results are distinct positive integers. These positive integers, together with $a_1, a_2, \ldots, a_n$, form the set of all positive integers from 1 to $S_n$.
(i) Find the values of $a_1$ and $a_2$.
(ii) Find the general term formula of the sequence.

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