
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 square $ABCD$, each side measures $10$ units. Point $E$ is on side $AB$, such that $AE = 3 \times EB$. Determine the ratio of the area of square $EFGH$, where each vertex $F$, $G$, and $H$ lies on sides $BC$, $CD$, and $DA$ respectively, to the area of square $ABCD$.
A) $\frac{1}{16}$
B) $\frac{1}{4}$
C) $\frac{3}{4}$
D) $\frac{1}{2}$
E) $\frac{9}{16}$

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