
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
Let  $ABCD$  be a unit square. For any interior points  $M,N$  such that the line  $MN$  does not contain a vertex of the square, we denote by  $s(M,N)$  the least area of the triangles having their vertices in the set of points  $\{ A,B,C,D,M,N\}$ . Find the least number  $k$  such that  $s(M,N)\le k$ , for all points  $M,N$ .

*Dinu Șerbănescu*

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