
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
Fyodor starts writing pairs of natural numbers $(a, b)$ on a board, where $a < b$ and each number does not exceed 2018. Furthermore, if a pair $(a, b)$ is already on the board, he cannot write any pair of the form $(c, a)$ or $(b, d)$. What is the greatest number of pairs he can write on the board?

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