
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
Geoff and Trevor each roll a fair eight-sided die with faces showing numbers from 1 to 8. What is the probability that the product of the numbers they roll is even? Additionally, what is the probability that the sum of the numbers they roll is even?

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