
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 $b_1, b_2, \dots, b_{50}$ be integers where each $b_i$ is equal to $-1$, $0$, $1$, or $2$. Moreover, the sum $b_1 + b_2 + \dots + b_{50}$ must be an even integer. Find the minimum positive value of \[\sum_{1 \le i < j \le 50} b_i b_j.\]

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