
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 cubical die has faces marked with the numbers $1$, $2$, $3$, $3$, $4$, and $4$. Another die has faces marked with the numbers $1$, $2$, $5$, $6$, $7$, and $9$. Calculate the probability that the sum of the top two numbers will be $6$, $8$, or $10$.

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