
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
Given that one die is marked with numbers $1$, $3$, $3$, $5$, $5$, and $7$, and the other die is marked with numbers $2$, $4$, $4$, $6$, $6$, and $8$, calculate the probability that the sum of the top faces equals $8$, $10$, or $12$.

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