
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
Triangle $ABC$ is a right triangle where $AB = AC$. Points $D$, $E$, and $F$ are the midpoints of $\overline{AB}$, $\overline{BC}$, and $\overline{CA}$, respectively. Point $G$ is the midpoint of segment $\overline{DF}$, and point $H$ is the midpoint of segment $\overline{DE}$. Determine the ratio of the area inside triangle $DEF$ to the area outside triangle $DEF$ but inside triangle $ABC$. Express your answer as a common fraction.

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