
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
Clarissa has an unfair six-sided die. The probabilities of rolling each number from 1 to 6 are as follows: 1 through 5 each have a probability of $\frac{1}{12}$, except number 3 which has a probability of $\frac{1}{6}$. The probability of rolling a 6 is $\frac{7}{12}$. 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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