
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
Two pairs of parallel lines are given: \( A B \parallel C D \) and \( A C \parallel B D \). Point \( E \) lies on the line \( B D \), point \( F \) is the midpoint of the segment \( B D \), point \( G \) is the midpoint of the segment \( C D \), and the area of triangle \( A C E \) is \( 20 \mathrm{~cm}^{2} \).

Determine the area of triangle \( D F G \).

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