
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 all terms of the sequence $\{a\_n\}$ are positive, its sum of the first $n$ terms is $S\_n$, and the point $(a\_n, S\_n)$ lies on the graph of the function $y = \frac{1}{8}x^2 + \frac{1}{2}x + \frac{1}{2}$, where $n \in \mathbb{N}^*$.

(I) Find the general formula for the sequence $\{a\_n\}$.
(II) Let $c\_n = \frac{1}{a\_n a\_{n+1}}$, find the sum of the first $n$ terms of the sequence $\{c\_n\}$, denoted as $T\_n$.

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