
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
Bob rolls a fair eight-sided die each morning, except on Sundays. If Bob rolls a composite number or a 1, he eats sweetened cereal. If he rolls a prime number, he eats unsweetened cereal. On Sundays, he eats the type of cereal he ate the most days in the past six days; if there's a tie, he favors unsweetened cereal. In a non-leap year, what is the expected value of the difference between the number of days Bob eats unsweetened cereal and the number of days Bob eats sweetened cereal?

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