
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. The numbers on the die follow this rule:
- If Alice rolls a prime number (2, 3, 5, 7), she drinks coffee.
- If she rolls a composite number (4, 6, 8), she drinks tea.
- If she rolls a 1, she rolls again.
For a non-leap year, calculate the expected number of days Alice drinks more coffee than tea.

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