
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 a numerical sequence $\left\{x_{n}\right\}$, in which all terms are distinct starting from $n \geq 2$, the relationship $x_{n} = \frac{x_{n-1} + 98 x_{n} + x_{n+1}}{100}$ holds. Find $\sqrt{\frac{x_{2023} - x_{1}}{2022} \cdot \frac{2021}{x_{2023} - x_{2}}} + 2021$.

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