
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 an arithmetic sequence $\{a\_n\}$ with the first term $1$ and a non-zero common difference, let $S\_n$ denote the sum of its first $n$ terms. Suppose $S\_2^2 = S\_1 \cdot S\_4$.

(1) Find the general term formula for the sequence $\{a\_n\}$.
(2) Let $b\_n = \frac{1}{a\_n a_{n+1}}$. Find the sum $T\_n$ of the first $n$ terms of the sequence $\{b\_n\}$.

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