
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
Alice rolls a fair eight-sided die each morning. If Alice rolls an odd number (but not 1), she has oatmeal; if she rolls an even number or 1, she rolls a second time:
- If the second roll is 1, she skips breakfast.
- Otherwise, she eats pancakes based on the second roll’s outcome; any number except 1 leads to pancakes.
In a non-leap year, what is the expected number of times Alice will roll her die?

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