
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 $f(x)=1+x+(1+x)^{2}+\ldots+(1+x)^{n} (x\neq 0,n\in\mathbb{N}^{*})$. The coefficient of the $x$ term in the expansion of $f(x)$ is denoted as $T_{n}$. Find the value of $\lim_{n\rightarrow \infty} \frac{T_{n}}{n^{2}}$.

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