
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
The sequence \(\left(x_{n}\right)\) is defined recursively by \(x_{0}=1, x_{1}=1\), and:

\[ x_{n+2}=\frac{1+x_{n+1}}{x_{n}} \]

for all \(n \geq 0\). Calculate \(x_{2007}\).

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