
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
Given that $BDEF$ is a rectangle and $AB = BC = 2$, find the number of square units in the area of the regular octagon created by extending lines from the rectangle's sides.

[asy]
real x = sqrt(8);
pair A,B,C,D,E,F,G,H;
F=(0,0); E=(4,0); D=(4+x,x); C=(4+x,4+x);
B=(4,4+2x); A=(0,4+2x); H=(-x,4+x); G=(-x,x);
draw(A--B--C--D--E--F--G--H--cycle);
draw((-x,0)--(4+x,0)--(4+x,4+2x)--(-x,4+2x)--cycle);
label("$B$",(-x,4+2x),NW); label("$D$",(4+x,4+2x),NE); label("$E$",(4+x,0),SE); label("$F$",(-x,0),SW);
label("$A$",(-x,x+4),W); label("$C$",(0,4+2x),N);
[/asy]

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