
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 five triangles formed with vertices A, B, C, D, and E. If each triangle has the same probability of being selected, what is the probability that a selected triangle includes vertex C? Express your answer as a common fraction.

[asy]
draw((0,0)--(2,0)--(1,1)--(0,0)--cycle,linewidth(1));
draw((0,0)--(1,0)--(1,1)--(0,0)--cycle,linewidth(1));
draw((1,0)--(2,0)--(1,1)--(1,0)--cycle,linewidth(1));

label("A",(0,0),SW);
label("B",(1,0),S);
label("C",(2,0),SE);
label("D",(1,1),N);
label("E",(0,1),NW);
[/asy]

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