
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
Two cubical dice, colored red and blue, with numbers $1$ through $6$ are used. All twelve numbers are removed, shuffled, then randomly reassigned to the dice, one number per face. Additionally, we consider a roll valid only if the number displayed on the red die is strictly greater than the number on the blue die. If the dice are rolled, what is the probability that the sum of the numbers displayed on the top faces equals $8$?
A) $\frac{1}{18}$
B) $\frac{1}{36}$
C) $\frac{1}{12}$
D) $\frac{1}{6}$

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