
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
Consider a diagram with four triangles formed by points A, B, C, D, and E. Points A, E, and C form a larger triangle, with points B and D located on line segment EC, where D is between E and C, and closer to E. A smaller triangle BDE is entirely shaded. If each triangle has the same probability of being selected, what is the probability that a selected triangle has all or part of its interior shaded? 

[asy]
draw((0,0)--(2,0)--(0,2)--(0,0)--cycle,linewidth(1));
draw((0,0)--(1,0)--(1,1)--(0,0)--cycle,linewidth(1));
draw((1,0)--(2,0)--(1,1)--cycle, gray, black);
draw((1,0)--(1.5,0)--(1,1)--cycle,linewidth(1));

label("A",(0,2),NW);
label("B",(1,1),N);
label("C",(2,0),SE);
label("D",(1.5,0),S);
label("E",(0,0),SW);
[/asy]

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