
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 $b_1,$ $b_2,$ $\dots,$ $b_{100}$ is $\pm 1.$  Find the smallest possible positive value of
\[\sum_{1 \le i < j \le 100} b_i b_j.\]

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