
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
An octagon $ABCDEFGH$ is divided into eight smaller equilateral triangles, such as $\triangle ABJ$ (where $J$ is the center of the octagon), shown in boldface in the diagram. By connecting every third vertex, we obtain a larger equilateral triangle $\triangle ADE$, which is also shown in boldface. Compute the ratio $[\triangle ABJ]/[\triangle ADE]$. 
[asy]
size(150); defaultpen(linewidth(0.8)); dotfactor=5;
pair[] oct = new pair[8];
string[] octlabels = {"$H$", "$G$", "$F$", "$E$", "$D$", "$C$", "$B$", "$A$"};
octlabels.cyclic=true;
oct[0] = dir(0);
for(int i = 1; i <= 8; ++i){
    oct[i] = dir(45*i);
    draw(oct[i] -- oct[i-1]);
    dot(octlabels[i],oct[i],oct[i]);
}
draw(oct[0]--oct[3]--oct[6]--cycle, linewidth(1.3));
draw(oct[0]--oct[1]--(0,0)--cycle, linewidth(1.3));
dot("$J$",(0,0),2*S);
[/asy]

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