
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 new diagram, there are four 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? The diagram is as follows:

[asy]
draw((0,0)--(2,0)--(1,2)--cycle,linewidth(1)); // Large triangle ABC
draw((1,0)--(1,2)--(0,0)--cycle,linewidth(1)); // Triangle ADB
label("A", (1,2), N);
label("B", (2,0), SE);
label("C", (0,0), SW);
label("D", (1,0), S);
filldraw((0,0)--(1,0)--(1,2)--cycle, gray, black); // Shaded triangle ADC
[/asy]

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