
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 a composite number, she drinks coffee. If she rolls a prime number, she drinks tea. If she rolls a 1, then she rolls again. In a non-leap year, what is the expected value of the difference between the number of days Alice drinks tea and the number of days she drinks coffee?

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