
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
Consider a cube $ABCDEFGH$ where each edge has length 2 units. Let point $K$ be the midpoint of edge $AB$ and point $L$ the midpoint of edge $GH$. If $M$ is the midpoint of segment $KL$ and $N$ is the midpoint of segment $CD$, determine the ratio $S$ of the area of rectangle $EMFN$ to the area of one face of the cube.

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