
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 $\{a\_n\}$ is an arithmetic sequence with positive terms, $S\_n$ is the sum of its first $n$ terms, and $4S\_n = (a\_n + 1)^2$.

(I) Find the values of $a\_1$, $a\_2$, and the general term formula for $\{a\_n\}$;

(II) Find the minimum value of the sequence $\{S\_n - \frac{7}{2}a\_n\}$.

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