
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 particularly unusual four-sided die is designed such that:
- It lands on Side 1 with probability $\frac{1}{4}$, winning you $2 dollars.
- It lands on Side 2 with probability $\frac{1}{4}$, winning you $4 dollars.
- It lands on Side 3 with probability $\frac{1}{3}$, causing you to lose $6 dollars.
- It lands on Side 4 with probability $\frac{1}{6}$, resulting in no change in your money.

What is the expected winnings from rolling this die? Express your answer as a dollar value.

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