
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
Five standard, six-sided dice are to be rolled. If the product of their values turns out to be an even number, what is the probability that their sum is even? Express your answer as a common fraction.

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