
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
A fair 8-sided die is rolled. If the roll is a multiple of 3, then you win that amount of dollars (for example, if you roll 6, then you win $\$6$). If the roll is not a multiple of 3, you win nothing. What is the expected value of your winnings? Express your answer as a dollar value.

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