
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 based on the previous problem, point F is added between points C and D. The triangles formed are ABE, ABF, AEF, BCF, BDF, and CDF. The shading remains the same, covering CDF. 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?

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