
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