
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 has an unfair six-sided die. The probabilities that it rolls a number from 1 to 5 are as follows: $\frac{1}{6}$ for a 1, $\frac{1}{8}$ for a 2, $\frac{1}{12}$ for a 3, $\frac{1}{12}$ for a 4, and $\frac{1}{12}$ for a 5. The probability that it rolls a 6 is adjusted accordingly. What is the expected value of the number shown when this die is rolled?

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