
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 $\left\{a_{n}\right\}$ where $a_{1}=1$ and $a_{n+1}=\frac{\sqrt{3} a_{n} - 1}{a_{n} + \sqrt{3}}$ for $n \in \mathbf{N}$, find the value of $a_{2004}$.

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