
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
Quadrilateral $ABCD$ is a rectangle, and segment $AE$ is perpendicular to segment $ED$. If $AE = 12$ units and $DE = 9$ units, what is the area of pentagon $AEDCB$, in square units? Assume that $AB = CD = 3 \times DE$ and $BC = DA = 2 \times AE$.

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