
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 \(x_n = \frac{x_{n-1} + 298x_n + x_{n+1}}{300}\) holds. Find \(\sqrt{\frac{x_{2023} - x_2}{2021} \cdot \frac{2022}{x_{2023} - x_1}} - 2023\).

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