
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 depicted below, there are total of six triangles formed by the given points. If each triangle has the same probability of being picked, what is the probability that a chosen triangle contains any shaded area?

[asy]
draw((0,0)--(2,0)--(1,2)--(0,0)--cycle,linewidth(1));
draw((1,0)--(1.5,1)--(0.5,1)--(1,0)--cycle,linewidth(1));
label("A",(1,2),N);
label("B",(2,0),SE);
label("C",(1,0),S);
label("D",(0,0),SW);
label("E",(0.5,1),NW);
label("F",(1.5,1),NE);
filldraw((1,0)--(2,0)--(1.5,1)--cycle,gray,black);
[/asy]

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