
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 the sequence $\left\{x_{n}\right\}$ where $x_{1} \in \mathbf{R}$ and $x_{n+1}=\frac{x_{n}^{3}+3 x_{n}}{3 x_{n}^{2}+1}$ for $n=1,2,\cdots$, discuss the monotonicity and the limit of the sequence.

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