
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
Angle $FAC$ is a right angle, and $CF=16$ units. What is the number of square units in the sum of the areas of the two squares $ABCD$ and $AEGF$?

[asy]
draw((0,0)--(3,0)--(3,4)--(0,4)--cycle);
draw((0,4)--(0,8)--(-4,8)--(-4,4)--cycle);
draw((0,4)--(0,8));
draw((3,0)--(3,4));

label("A", (0,4), W);
label("B", (0,0), S);
label("C", (3,0), SE);
label("D", (3,4), NE);
label("E", (0,8), N);
label("F", (-4,8), NW);
label("G", (-4,4), SW);
label("16", (1.5, 2), E);
[/asy]

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