
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
Roll a die (marked with numbers 1, 2, 3, 4, 5, 6 on its six faces):
(I) If you roll the die consecutively twice, what is the probability that the numbers facing up are different?
(II) If you roll the die consecutively twice, what is the probability that the sum of the numbers facing up is 6?
(III) If you roll the die consecutively five times, what is the probability that an odd number faces up exactly three times?

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