
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
Three equilateral triangles $ABC$, $BCD$, and $CDE$ are positioned such that $B$, $C$, and $D$ are collinear, and $C$ is the midpoint of $BD$. Triangle $CDE$ is positioned such that $E$ is on the same side of line $BD$ as $A$. What is the value of $AE \div BC$ when expressed in simplest radical form?

[asy]
draw((0,0)--(5,8.7)--(10,0)--cycle);
draw((10,0)--(12.5,4.35)--(15,0)--cycle);
label("$A$",(0,0),SW);
label("$B$",(5,8.7),N);
label("$C$",(10,0),S);
label("$D$",(15,0),SE);
label("$E$",(12.5,4.35),N);
[/asy]

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