
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 $a_n$ is the coefficient of the $x^2$ term in the expansion of $(2+x)^n$ (where $n \in \mathbb{N}^*$, $n \geq 2$, and $x \in \mathbb{R}$), find the limit as $n$ approaches infinity:
$$
\lim_{n \to \infty}\left( \frac{2^{2}}{a_{2}} + \frac{2^{3}}{a_{3}} + \ldots + \frac{2^{n}}{a_{n}} \right).
$$

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