
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 several triangles. If each triangle has the same probability of being selected, what is the probability that a selected triangle includes the point G (which is shaded)? Express your answer as a common fraction.

[asy]
draw((0,1)--(1,1)--(1,0)--(0,0)--cycle,linewidth(1));
draw((0,1)--(0.5,0.5)--(1,1)--cycle,linewidth(1));
draw((0,0)--(0.5,0.5)--(1,0)--cycle,linewidth(1));

label("A",(0,1),NW);
label("B",(1,1),NE);
label("C",(1,0),SE);
label("D",(0,0),SW);
label("E",(0.5,0.5),N);

filldraw(circle((0.5,0.5),0.1),black);     // Shaded point G
[/asy]

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