
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
Rectangle $ABCD$ has dimensions such that $AB = 15$ units and $BC = 10$ units. Segment $AE$ is perpendicular to segment $ED$ with $AE = 9$ units and $DE = 12$ units. Find the area of pentagon $AEDCB$.

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