
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
Cutting isosceles right triangle $BFC$ out of square $ABCD$ and translating it leftwards creates the shape $ABFCDE$. The perimeter of square $ABCD$ is 40 inches. What is the perimeter, in inches, of $ABFCDE$?

[asy]
import graph;
filldraw((0,0)--(sqrt(2)*2,2)--(2+2sqrt(2),2)--(2sqrt(2),0)--(2+2sqrt(2),-2)--(sqrt(2)*2,-2)--cycle,grey,linewidth(1));
draw((sqrt(2)*2,2)--(sqrt(2)*2,-2),linewidth(1));
draw((2+2sqrt(2),-2)--(2+2sqrt(2),2)--(2sqrt(2),0)--(2+2sqrt(2),-2)--cycle,dashed);

label("A",(sqrt(2)*2,2),N);
label("B",(2+2sqrt(2),2),N);
label("C",(2+2sqrt(2),-2),S);
label("D",(sqrt(2)*2,-2),S);
label("E",(0,0),W);
label("F",(2sqrt(2),0),N);
[/asy]

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