
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 the sequence \(\left\{x_{n}\right\}\), and
\[ x_{n+1} = \frac{x_{n}+(2-\sqrt{3})}{1-(2-\sqrt{3}) x_{n}}, \]

find the value of \(x_{1001} - x_{401}\).

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