
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 $\{a\_n\}$ that satisfies $a_{n+1} + a_n = 4n - 3$, $n \in \mathbb{N}^*$
(1) If the sequence $\{a\_n\}$ is an arithmetic sequence, find the value of $a\_1$;
(2) When $a\_1 = -3$, find the sum of the first $n$ terms of the sequence, $S\_n$;
(3) If $\frac{a\_n^2 + a_{n+1}^2}{a\_n + a_{n+1}} \geq 5$ holds for any $n \in \mathbb{N}^*$, find the range of values for $a\_1$.

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