
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
Rectangle $ABCD$ contains three shapes within: squares $ABEF$ and $CDGH$, and right triangle $EFG$. Point $E$ is the midpoint of $AB$, point $G$ is the midpoint of $CD$, and point $F$ lies on $BC$ such that $BF = FC = \frac{1}{2}BC$. What is the ratio of the area of triangle $EFG$ to the total area of the rectangle?
A) $\frac{1}{10}$
B) $\frac{1}{8}$
C) $\frac{1}{6}$
D) $\frac{1}{4}$
E) $\frac{1}{2}$

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