
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 peculiar dice operates in a strange manner, offering three possible outcomes when rolled: it shows a star with probability $\frac{1}{4}$, a moon with probability $\frac{1}{2}$, and a sun with probability $\frac{1}{4}$. If it shows a star, you win 2 dollars. If it shows a moon, you win 4 dollars. However, if it shows a sun, you lose 6 dollars. What is your expected winnings from rolling this dice once? Express your answer as a dollar value.

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