
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 $AF$ is perpendicular to segment $FD$. If $AF = 12$ units and $FD = 9$ units, what is the area of pentagon $AFDCB$, in square units? [asy]
size(150);
pair A, B, C, D, F;
A=(0,15);
B=(0,0);
C=(15,0);
D=(15,15);
F=(12,9);
draw(A--B--C--D--A);
draw(A--F--D);
label("A", A, NW);
label("B", B, SW);
label("C", C, SE);
label("D", D, NE);
label("F", F, S);
[/asy]

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