
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 rectangular prism has dimensions 3 units, 4 units, and 5 units. Three distinct vertices of this prism are chosen at random. What is the probability that the plane determined by these three vertices intersects the interior of the prism?
A) $\frac{3}{7}$
B) $\frac{4}{9}$
C) $\frac{4}{7}$
D) $\frac{5}{7}$
E) $\frac{1}{2}$

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