
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 $ABCD$ with $AB$ parallel to $CD$ and the diagonals $AC$ and $BD$ intersecting at $E$, suppose the area of triangle $ABE$ is 45 square units, and the area of triangle $ADE$ is 15 square units. Additionally, it is given that the length ratio of $DE$ to $BE$ is $1:3$. What is the area of trapezoid $ABCD$?

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