
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 dice with a different number of faces are rolled. Dice A has at least 7 faces and Dice B has at least 5 faces. Each face of Dice A is distinctly numbered from 1 up to the number of faces on Dice A, and similarly for Dice B. The probability of rolling a sum of 13 is twice the probability of rolling a sum of 8. If the probability of rolling a sum of 16 is exactly $\frac{1}{20}$, what is the least possible number of faces on the two dice combined?
A) 22
B) 23
C) 24
D) 25
E) 26

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