
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 \( \frac{M(S)}{m(S)} \)?

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