
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 a new diagram, there are five points labeled F, G, H, I, and J forming the following triangles: FGJ, FGH, GHI, HIJ, and FIJ. One triangle, GHI, is shaded completely. If each triangle has the same probability of being selected, what is the probability that a selected triangle is shaded? Express your answer as a common fraction.

[asy]
draw((0,0)--(2,0)--(1,2)--cycle,linewidth(1));  // Triangle FGJ
draw((0,0)--(1,1)--(1,2)--cycle,linewidth(1));  // Triangle FGH
draw((1,1)--(2,0)--(1,2)--cycle, gray, black);  // Triangle GHI, shaded
draw((1,1)--(2,0)--(3,1)--cycle,linewidth(1));  // Triangle HIJ
draw((0,0)--(1,2)--(3,1)--cycle,linewidth(1));  // Triangle FIJ

label("F",(0,0),SW);
label("G",(1,1),S);
label("H",(1,2),N);
label("I",(2,0),SE);
label("J",(3,1),E);
[/asy]

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