
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 similar diagram, there are three points \(A\), \(B\), \(C\) forming a large triangle. Inside this large triangle, a smaller triangle \(DEF\) is placed such that \(D\) is on \(AB\), \(E\) is on \(BC\), and \(F\) is on \(AC\). The triangle \(DEF\) is completely shaded. If each triangle formed by combining any of the points \(A, B, C, D, E, F\) has the same probability of being selected, what is the probability that a selected triangle has all or part of its interior shaded? Express your answer as a common fraction.

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