
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
In the diagram, there are more than five triangles. 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? Express your answer as a common fraction.

[asy]
draw((0,0)--(1,0)--(0,1)--cycle, linewidth(1)); // Big triangle
draw((0,0)--(0.5,0)--(0.5,0.5)--cycle, linewidth(1)); // Small triangle inside
draw((0.5,0.5)--(1,0)--(0.5,0)--cycle, linewidth(1)); // Additional triangle
label("A", (0,1), NW);
label("B", (0.5,0.5), NE);
label("C", (1,0), SE);
label("D", (0.5,0), S);
label("E", (0,0), SW);
label("F", (0.75,0), S);
draw((0.5,0)--(0.75,0)--(0.5,0.5)--cycle, linewidth(1)); // Another small triangle
filldraw((0.5,0)--(1,0)--(0.5,0.5)--cycle,gray,black); // Shaded part
[/asy]

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