
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 now rolls a fair eight-sided die each morning. His die sides are numbered from 1 to 8. If Bob rolls a number less than 5, he eats organic cereal. If Bob rolls a number 5 or greater, he eats gluten-free cereal. If Bob rolls an 8, then he rolls again. In a non-leap year, what is the expected value of the difference between the number of days Bob eats organic cereal and the number of days he eats gluten-free cereal?

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