
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 die has three outcomes: landing 1, landing 2, and landing 3. The probabilities of landing on 1, 2, and 3 are $\frac{1}{4}$, $\frac{1}{2}$, and $\frac{1}{4}$ respectively. If it lands on 1, you win 2 dollars. If it lands on 2, you win 5 dollars. If it lands on 3, you lose 10 dollars. What is the expected winnings from throwing this die? Express your answer in dollars, rounded to the nearest cent.

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