
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 $\{a_n\}$, $a_1=1$, and $a_n= \dfrac{n^2}{n^2-1}a_{n-1} (n\geqslant 2,n\in\mathbb{N}^*)$, then the sum of the first $n$ terms of the sequence $\left\{ \dfrac{a_n}{n^2} \right\}$, denoted as $T_n=$

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