
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
In the sequence $\{a_n\}$, $a_1 = \frac{1}{2}$, and the point $(a_n, a_{n+1})$ (where $n \in \mathbb{N}^*$) lies on the line $y = x + \frac{1}{2}$.  
(I) Find the general term formula for the sequence $\{a_n\}$.  
(II) Let $b_n = \frac{1}{a_n \cdot a_{n+1}}$, find the sum of the first $n$ terms, $T_n$, of the sequence $\{b_n\}$.

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