
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
On the blackboard, there is a sequence of numbers: \(1, 2, 3, \cdots, 2018, 2019\). You can erase any number of these numbers and write the remainder when the sum of the erased numbers is divided by 17 (if it's divisible, write 0). Continue with this operation until there is only one number left on the blackboard. What is this final number?

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