
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 a sequence $\\{a\_n\\}$ where all terms are positive numbers. Let $S\_n$ denote the sum of the first $n$ terms, and it is given that $S\_n = \frac{a\_n(a\_n+1)}{2}$, $n \in \mathbb{N}^*$.

(1) Find the general term formula for the sequence $\\{a\_n\\}$.

(2) Let $b\_n = \frac{1}{a\_n \cdot a\_{n+1}}$ and $T\_n = b\_1 + b\_2 + \dots + b\_n$. Find $T\_n$.

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