
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
The sequence $\left\{x_{n}\right\}$ satisfies $x_{1}=1$, and for any $n \in \mathbb{Z}^{+}$, it holds that $x_{n+1}=x_{n}+3 \sqrt{x_{n}}+\frac{n}{\sqrt{x_{n}}}$. Find the value of $\lim _{n \rightarrow+\infty} \frac{n^{2}}{x_{n}}$.

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