
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 special dice, when rolled, can result in three different outcomes: it shows a 6 with a probability of $\frac{1}{4}$, a number less than 6 but greater than 1 with a probability of $\frac{1}{2}$, and a 1 with a probability of $\frac{1}{4}$. If it shows a 6, you win 4 dollars. If it shows any number from 2 to 5, you win 2 dollars. But if it shows a 1, you lose 6 dollars. What is your expected winnings from rolling this dice?

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