
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 $CF = 12$ 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)--(1,1)--(0,2)--(-1,1)--cycle);
draw((0,2)--(2,4)--(0,6)--(-2,4)--cycle);
draw((1,1)--(2,4));
draw((-1,1)--(-2,4));

label("A", (0,2), S);
label("C", (1,1), SE);
label("D", (0,0), S);
label("B", (-1,1), SW);
label("F", (2,4), NE);
label("G", (0,6), N);
label("E", (-2,4), NW);
label("12", (1.5, 2.5), SE);
[/asy]

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