
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 the sum of the first $n$ terms of a sequence $\left\{a_{n}\right\}$ is $S_{n}=\dfrac{3n^{2}-n}{2}$.
(1) Find the general formula for $\left\{a_{n}\right\}$;
(2) Let $b_{n}=\dfrac{1}{a_{n}a_{n+1}}$, and the sum of the first $n$ terms of the sequence $\left\{b_{n}\right\}$ is $T_{n}$. If $t\leqslant 4T_{n}$ holds for all $n\in N^{*}$, find the maximum value of the real number $t$.

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