
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 trapezoid $ABCD$ the lengths of the bases $AB$ and $CD$ are 9 and 27 respectively. The legs of the trapezoid $AD$ and $BC$ are extended to meet at point $F$ above line $CD$. An additional point $G$ on line $AD$ is such that $DG$ and $AD$ form a 1:2 ratio. Calculate the ratio of the area of triangle $FBG$ to the area of the trapezoid $ABCD$.

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