
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
Right triangle $ABC$ has a right angle at $C$ and $\overline{DE}$, $\overline{FG}$ are parallel to $\overline{AB}$, with $AD = DF = FB$. If $\overline{AB} = 8$ and $\overline{BC} = 6$, find the ratio of the area of trapezoid $FGAB$ to the area of triangle $ABC$.

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