
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
Every positive integer is marked with a number from the set \(\{0,1,2\}\), according to the following rule:

If a positive integer \(k\) is marked with \(j\), then the integer \(k+j\) is marked with 0.

Let \(S\) denote the sum of marks of the first 2019 positive integers. Determine the maximum possible value of \(S\).

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