
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 a sequence \( x_{1}, x_{2}, \cdots, x_{n}, \cdots \) where the sum of any three consecutive terms is 20, and \( x_{4} = 9 \) and \( x_{12} = 7 \), find the value of \( x_{2000} \).

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