
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 $\{a_n\}$, where $S_n$ is the sum of its first $n$ terms, and $a_2+a_6=6$, $S_3=5$.

(I) Find the general formula for the sequence $\{a_n\}$.

(II) Let $b_n= \dfrac {1}{a_{n-1}a_{n}}(n\geqslant 2),b_{1}=3,T_{n}=b_{1}+b_{2}+\ldots+b_{n}$. If $T_{n} < m$ holds for all $n\in\mathbb{N}^{*}$, find the minimum value of $m$.

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