
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
$ABCD$ is a trapezium with $AB//DC$ and $AB > DC$. $E$ is a point on $AB$ such that $AE = DC$. $AC$ meets $DE$ and $DB$ at $F$ and $G$ respectively. Find the value of $\frac{AB}{CD}$ for which $\frac{\text{Area of } \triangle DFG}{\text{Area of trapezium } ABCD}$ is maximum.

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