
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 numerical sequence \( \{x_n\} \), where all terms starting from \( n \geq 2 \) are distinct, the relation \( x_{n} = \frac{x_{n-1} + 198 x_{n} + x_{n+1}}{200} \) holds. Find \( \sqrt{\frac{x_{2023} - x_{1}}{2022} \cdot \frac{2021}{x_{2023} - x_{2}}} + 2022 \).

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