
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
Mike has an unfair eight-sided die. The probabilities of the die are as follows: Rolling a 1 occurs with a probability of $\frac{3}{20}$, a 2 with $\frac{1}{20}$, a 3 with $\frac{1}{20}$, a 4 with $\frac{1}{20}$, a 5 with $\frac{1}{10}$, a 6 with $\frac{1}{5}$, a 7 with $\frac{1}{10}$, and an 8 with $\frac{3}{10}$. What is the expected value of the number shown when this die is rolled?

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