
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
In cube $ABCDEFGH$ where $JKLM$ are midpoints of edges $AB$, $CD$, $EF$, and $GH$ respectively, and $N$ and $O$ are midpoints of segments $\overline{JM}$ and $\overline{KL}$, calculate the ratio $R$ of the area of quadrilateral $ANCO$ to the area of one of the faces of the cube.
A) $\frac{1}{3}$
B) $\frac{1}{4}$
C) $\frac{1}{2}$
D) $\frac{2}{3}$
E) $\frac{1}{8}$

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