
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 selected on the sides $AB$ and $BC$ of rectangle $ABCD$, respectively. From point $F$, a perpendicular $FK$ is dropped to side $CD$. From point $G$, a perpendicular $GH$ is dropped to side $AD$. The intersection point of $FK$ and $GH$ is denoted as $E$. Find the area of triangle $DFG$, given that the areas of rectangles $ABCD$ and $HEK$ are 20 and 8, respectively.

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