
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 any 4 distinct points \(P_{1}, P_{2}, P_{3}, P_{4}\) on a plane, find the minimum value of the ratio
\[ 
\frac{\sum_{1 \leq i < j \leq 4} P_{i}P_{j}}{\min_{1 \leq i < j \leq 4} P_{i}P_{j}} 
\]

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