
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
Consider a scenario where a cubical die is labeled with the numbers $2$, $3$, $3$, $4$, $4$, and $5$. Another die is marked with $1$, $2$, $3$, $5$, $6$, and $7$. Calculate the probability that rolling these two dice simultaneously results in a sum on their top faces of either $6$, $8$, or $10$.

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