
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
Regular octagon $ABCDEFGH$ is divided into eight smaller congruent triangles, such as $\triangle ABJ$, shown in boldface in the diagram. By connecting every third vertex, we obtain a larger equilateral triangle $\triangle ADE$, 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 = {"$A$","$B$","$C$","$D$","$E$","$F$","$G$","$H$"};
octlabels.cyclic=true;
oct[0] = dir(45);
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}
user