
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
Let $S_{n}$ be the sum of the first $n$ terms of the arithmetic sequence ${a_{n}}$. Given that $a_{1}+a_{13}=26$ and $S_{9}=81$.

(I) Find the general term formula for ${a_{n}}$.

(II) Let $b_{n}=\dfrac{1}{{a_{n+1}}{a_{n+2}}}$ and $T_{n}=b_{1}+b_{2}+…+b_{n}$. If $30T_{n}-m\leqslant 0$ holds for all $n∈N^{*}$, find the minimum value of the real number $m$.

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