
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 set  $S$  of five points in the plane, no three of which are collinear, let  $M(S)$  and  $m(S)$  denote the greatest and smallest areas, respectively, of triangles determined by three points from  $S$ .  What is the minimum possible value of  $M(S)/m(S)$  ?

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