
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
In a plane, 4 points \( A_{1}, A_{2}, A_{3}, A_{4} \) are given, and the distance between any two of them is at least 1. What is the maximum possible number of line segments \( A_{i}A_{j} \) with a length of 1 that can be drawn between these points?

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