
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
Consider the sequence $\{a\_n\}$ that satisfies: $a_{n+1} = 4 + a\_n$, and $a\_1 = 1$.
(1) Find the general formula for the $n$-th term of the sequence;
(2) If $b\_n$ is the geometric mean of $a\_n$ and $a_{n+1}$, find the sum of the first $n$ terms, denoted as $T\_n$, for the sequence $\{ \frac{1}{b\_n^2} \}$.

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