
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
The area of parallelogram $ABCD$ is $10$, with side lengths $AB=3$ and $BC=5$. Points $E$, $F$, and $G$ are located on $AB$, $BC$, and $AD$ respectively, such that $AE=BF=AG=2$. Line $GH$ is drawn parallel to $EF$ and intersects $CD$ at point $H$. Find the area of quadrilateral $EFHG$.

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