
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
Gina owns an unfair eight-sided die. The probability that it rolls an 8 is $\frac{1}{3}$, and each of the numbers 1 through 7 has an equal probability of coming up when the die is rolled. What is the expected value of the number shown when this die is rolled?

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