
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 magical four-sided coin lands on side A with probability $\frac{1}{4}$, side B with probability $\frac{1}{4}$, side C with probability $\frac{1}{3}$, and disappears with probability $\frac{1}{6}$. If it lands on side A, you win 2 dollars. If it lands on side B, you lose 1 dollar. If it lands on side C, you win 4 dollars. If the coin disappears, you lose 3 dollars. What is your expected earnings from flipping this coin?

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