
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 roll is even, then you win twice the amount of the number rolled in dollars (for example, if you roll a 4, then you win $8). If you roll an 8, you additionally win a $5 bonus on top of the doubled roll value. If the roll is odd, you win nothing. Calculate the expected value of your winnings in dollars.

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