
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  $a_1, a_2,...,a_{2018}$  be a sequence of numbers such that all its elements are elements of a set  $\{-1,1\}$ . Sum   $$ S=\sum \limits_{1 \leq i < j \leq 2018} a_i a_j $$   can be negative and can also be positive. Find the minimal value of this sum 

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