
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
Triangle \( A B C \) is divided by line segments as shown in the picture. Line segments \( D E \) and \( A B \) are parallel. Triangles \( C D H, C H I, C I E, \) and \( F I H \) have the same area of \( 8 \, \mathrm{dm}^2 \).

Determine the area of quadrilateral \( A F H D \).

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