
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 $$\lim_{n \to \infty} \frac{T_n}{n^2} = \_\_\_\_\_\_.$$

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