
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 triangle $ABC$, where $\angle ABC = 90^\circ$, $AB = 6$ cm, and $BC = 8$ cm. Points $D$, $E$, and $F$ are the midpoints of sides $AC$, $AB$, and $BC$, respectively. Define point $G$ as the midpoint of segment $DF$ and point $H$ as the midpoint of segment $EF$. Calculate the ratio of the area of quadrilateral $ADHE$ to the area of triangle $ABC$.

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