
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
For the infinite sequence of numbers \( x_{1}, x_{2}, x_{3}, \ldots \), the relationship \( x_{n} = x_{n-1} \cdot x_{n-3} \) holds for all natural numbers \( n \geq 4 \). It is known that \( x_{1} = 1 \), \( x_{2} = 1 \), and \( x_{3} = -1 \). Find \( x_{2022} \).

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