
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 $ABC$, $AB = AC = 10$ cm, and $BC = 10\sqrt{2}$ cm, making it a right isosceles triangle. Points $D$, $E$, and $F$ are the midpoints of sides $AB$, $BC$, and $AC$, respectively. A point $J$ is the midpoint of segment $DE$. Calculate the area of the quadrilateral $DFEJ$.

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