
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
An 8-sided die is rolled. If the even number rolled is 4 or less, you win that amount in dollars; if the number is 6, you win twice that amount ($\$12$); if the number is 8, you win half the amount ($\$4$). If the roll is odd, you still 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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