
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 square, and segment $AE$ is perpendicular to segment $ED$. If $AE = 12$ units and $DE = 16$ units, what is the area of pentagon $AEDCB$? Consider the diagram remains the same.
```
[asy]
size(150);
pair A, B, C, D, E;
A=(0,14);
B=(0,0);
C=(14,0);
D=(14,14);
E=(11.2,7.8);
draw(A--B--C--D--A);
draw(A--E--D);
label("A", A, NW);
label("B", B, SW);
label("C", C, SE);
label("D", D, NE);
label("E", E, S);
[/asy]
```

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