
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
There is a sequence of numbers: \(1, 3, 8, 22, 60, 164, 448, \cdots\). The first number is 1, the second number is 3, and from the third number onwards, each number is exactly twice the sum of the previous two numbers. What is the remainder when the 2000th number in this sequence is divided by 9?

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