
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 the cube $ABCDEFGH$ with side length $2$, let $M$ and $N$ be the midpoints of $\overline{AB}$ and $\overline{GH}$, respectively. Let $P$ and $Q$ be the midpoints of $\overline{AD}$ and $\overline{EF}$. Determine the ratio $S$ of the area of the quadrilateral $MNPQ$ to the total surface area of the cube.
A) $\frac{\sqrt{45}}{48}$
B) $\frac{\sqrt{61}}{48}$
C) $\frac{\sqrt{75}}{48}$
D) $\frac{\sqrt{91}}{48}$

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