
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
Find \( x_{1000} \) if \( x_{1} = 4 \), \( x_{2} = 6 \), and for any natural number \( n \geq 3 \), \( x_{n} \) is the smallest composite number greater than \( 2 x_{n-1} - x_{n-2} \).

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