
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 strange dice has six sides, and when rolled, it can land on 1 or 2 with a probability of $\frac{1}{4}$ each, on 3 or 4 with a probability of $\frac{1}{6}$ each, and on 5 or 6 with a probability of $\frac{1}{8}$ each. If it lands on an odd number, I win 2 dollars. If it lands on an even number, I win 4 dollars. If it lands on the number 6, I lose 6 dollars besides the normal winning for an even number. What is the expected winnings from rolling this dice?

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