
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
You roll a fair 8-sided die (sides numbered 1 to 8). If the result of the roll is even, you win double the amount in dollars of the result (e.g., if you roll 4, you win $8). If the roll is odd, 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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