
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. If Bob rolls a composite number (4, 6, 8), he eats sweetened cereal. If he rolls a prime number (2, 3, 5, 7), he eats unsweetened cereal. If Bob rolls a 1, then he rolls again. If he rolls any number greater than 6, he eats yogurt. In a non-leap year, calculate the expected number of times Bob will roll his die.

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