
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
The side length of a regular octagon is 12 cm. What is the number of square centimeters in the area of the shaded region? Express your answer in simplest radical form.

[asy]
size(100);

pair A,B,C,D,E,F,G,H;
A = dir(45); B = dir(90); C = dir(135); D = dir(180); E = dir(225); F = dir(270); G = dir(315); H = dir(360);

fill(B--C--G--H--cycle,heavycyan);

draw(A--B--C--D--E--F--G--H--A);
[/asy]

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