
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
Let $a_{0}=0, a_{1}=1$, and $a_{n+2}=a_{n+1}+a_{n}$ for $n=0,1,2,\ldots$. Additionally, let $x_{1} \in \mathbf{R}$ and $x_{n}=\frac{a_{n-1}+a_{n-2} \cdot x_{1}}{a_{n}+a_{n-1} \cdot x_{1}}$ for $n=2,3,\ldots$. Given that $x_{2004}=\frac{1}{x_{1}}-1$, find $x_{1}$.

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