
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
Diana and Apollo each roll a die. Diana uses a regular 10-sided die (numbers 1 to 10), and Apollo uses a standard 6-sided die. What is the probability that Diana's number is larger than Apollo's number?
A) $\frac{1}{3}$ 
B) $\frac{15}{36}$
C) $\frac{13}{20}$
D) $\frac{1}{2}$
E) $\frac{5}{12}$

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