
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 square and $AB = BC = 1.5$, find the number of square units in the area of the regular octagon.

[asy]
real x = sqrt(2.25);
pair A,B,C,D,E,F,G,H;
F=(0,0); E=(2.25,0); D=(2.25+x,x); C=(2.25+x,2.25+x);
B=(2.25,2.25+2.25x); A=(0,2.25+2.25x); H=(-x,2.25+x); G=(-x,x);
draw(A--B--C--D--E--F--G--H--cycle);
draw((-x,0)--(2.25+x,0)--(2.25+x,2.25+2.25x)--(-x,2.25+2.25x)--cycle);
label("$B$",(-x,2.25+2.25x),NW); label("$D$",(2.25+x,2.25+2.25x),NE); label("$E$",(2.25+x,0),SE); label("$F$",(-x,0),SW);
label("$A$",(-x,x+2.25),W); label("$C$",(0,2.25+2.25x),N);
[/asy]

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