
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
George now has an unfair eight-sided die. The probabilities of rolling each number from 1 to 5 are each $\frac{1}{15}$, the probability of rolling a 6 or a 7 is $\frac{1}{6}$ each, and the probability of rolling an 8 is $\frac{1}{5}$. What is the expected value of the number shown when this die is rolled? Express your answer as a decimal.

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