
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
Points $F$ and $G$ are chosen on the sides $A B$ and $B C$ of rectangle $A B C D$, respectively. From point $F$, a perpendicular $F K$ is dropped to side $C D$, and from point $G$, a perpendicular $GH$ is dropped to side $AD$. The intersection of $F K$ and $GH$ is denoted as $E$. Find the area of triangle $D F G$, given that the areas of rectangles $A B C D$ and $H E K D$ are 20 and 8, respectively.

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