
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
Each of the numbers $a_1, a_2, \dots, a_{100}$ is either $+1$ or $-1$. Find the smallest possible positive value of 
\[
\sum_{1 \leq i < j \leq 100} a_i a_j.
\]

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