
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
Let  $C$  be a cube.  Let  $P$ ,  $Q$ , and  $R$  be random vertices of  $C$ , chosen uniformly and independently from the set of vertices of  $C$ .  (Note that  $P$ ,  $Q$ , and  $R$  might be equal.)  Compute the probability that some face of  $C$  contains  $P$ ,  $Q$ , and  $R$ .   

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