
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
A pentagonal pyramid has a pentagonal base and a vertex linking the center of the base to the apex. If three vertices are chosen at random, what is the probability that the plane determined by these three vertices contains points inside the pyramid?
A) \(\frac{1}{2}\) \\
B) \(\frac{1}{4}\) \\
C) \(\frac{3}{4}\) \\
D) \(\frac{2}{3}\) \\
E) \(\frac{2}{5}\)

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