
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
Find the number of units in the length of diagonal $AC$ of a regular octagon shown. Express your answer in simplest radical form. [asy]
size(120);
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);
draw(A--B--C--D--E--F--G--H--cycle);
draw(A--E);
label("12",(A+B)/2,NE);
label("$A$",A,E);
label("$C$",E,W);
[/asy]

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