
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
Let $A_{1}, A_{2}, \cdots, A_{n}$ be subsets of $\{1, 2, \cdots, 2018\}$ with exactly two elements each, such that the sets $A_{i} + A_{j}$ (where $1 \leq i \leq j \leq n$) are all distinct. Here,
$$
A + B = \{a + b \mid a \in A, b \in B\}.
$$

Find the maximum possible value of $n$.

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