
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 isosceles triangle with $AB=BC$. Points $D$, $E$, and $F$ are such that $D$ is the midpoint of hypotenuse $AC$, $E$ is one third along the side $BC$ from $B$ to $C$, and $F$ is the midpoint of side $AB$. Let $G$ be the midpoint of segment $DF$. What is the ratio of the area of triangle $DFE$ to the area of triangle $ABC$? Express your answer as a common fraction.

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