
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 fair dice, each with a different number of faces, are rolled. On each face of each die is printed a distinct integer from 1 to the number of faces on that die, inclusive. The probability of rolling a sum of $8$ is half the probability of rolling a sum of $11$, and the probability of rolling a sum of $15$ is $\frac{1}{15}$. What is the least possible number of faces on the two dice combined?
A) 17
B) 18
C) 19
D) 20
E) 21

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