
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 six-sided die each morning. If Bob rolls an even number greater than 2, he eats sweetened cereal. If he rolls an odd number greater than 2, he eats unsweetened cereal. If Bob rolls a 1 or a 2, then he rolls again. In a leap year, what is the expected number of times Bob will roll his die?

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