
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
Given that quadrilateral \(ABCD\) is a right trapezoid with the upper base \(AD = 8\) cm, the lower base \(BC = 10\) cm, and the right leg \(CD = 6\) cm. Point \(E\) is the midpoint of \(AD\), and point \(F\) is on \(BC\) such that \(BF = \frac{2}{3} BC\). Point \(G\) is on \(DC\) such that the area of triangle \(DEG\) is equal to the area of triangle \(CFG\). Find the area of triangle \(ABG\) in square centimeters.

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