
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 die has faces numbered $1$, $2$, $3$, $3$, $4$, and $4$. Another die has faces numbered $2$, $3$, $5$, $6$, $7$, and $8$. Determine the probability that the sum of the top two numbers when both dice are rolled will be either $6$, $8$, or $10$.
A) $\frac{1}{36}$
B) $\frac{1}{18}$
C) $\frac{11}{36}$
D) $\frac{5}{36}$
E) $\frac{1}{6}$

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