
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
For four distinct points \( P_{1}, P_{2}, P_{3}, P_{4} \) on a plane, find the minimum value of the ratio \( \frac{\sum_{1 \leqslant i<j \leqslant 4} P_{i} P_{j}}{\min_{1 \leqslant j \leqslant 4} P_{i} P_{j}} \).

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