
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 triangles. 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? The diagram consists of points A, B, C, D, and E arranged as follows:
- A is at the top,
- B and C are midpoints on the left and right side respectively,
- D is at the bottom left and E is at the bottom right.
Triangles within the diagram are ABD, ABE, ACD, ACE, and BDE. The shaded regions are within triangles ABD and ACE.

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