
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 has an eight-sided die with sides numbered from 1 to 8. Every morning, he rolls the die to decide his breakfast:
- If he rolls a composite number, he chooses sweetened cereal.
- If he rolls a prime number, he goes for unsweetened cereal.
- If he rolls a 1, 7, or 8, he needs to roll the die again.
What is the expected number of times Bob will roll his die in a non-leap year?

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