
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 \( x_{1} = 1 \), \( x_{2} = 2 \), and \( x_{n+2} = \frac{x_{n+1}^{2} - 7}{x_{n}} \left( n \in \mathbf{N}^{*} \right) \), find the smallest positive period of the sequence \( \left\{ x_{n} \right\} \).

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