
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 the isosceles trapezoid \( ABCD \) as shown, the top base \( AB \) is 4 cm, the bottom base \( CD \) is 12 cm, and the angle between the leg \( AD \) and the bottom base \( DC \) is \( 45^{\circ} \). If \( AF = FE = ED \) and \( BC = 4BG \), then the area of \(\triangle EFG\) is ______ square centimeters.

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