
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 the sequence $\left\{x_{n}\right\}$ be defined such that $x_{1}=5$, and
$$
x_{n+1}=x_{n}^{2}-2 \quad \text{for} \quad n=1,2, \ldots
$$

Find: 
$$
\lim _{n \rightarrow \infty} \frac{x_{n+1}}{x_{1} x_{2} \cdots x_{n}}
$$

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