
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 $\{a_n\}$, $(a_1=\frac{1}{2})$, the point $(a_n,a_{n+1})(n\in \mathbb{N}^*)$ is 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 of the sequence $\{b_n\}$, denoted as $T_n$.

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