
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 weighted coin has four outcomes: it comes up heads with probability $\frac{3}{8}$, tails with probability $\frac{1}{4}$, lands on its edge with probability $\frac{1}{8}$, and sometimes disappears with probability $\frac{1}{4}$. Winning conditions are as follows: if the coin shows heads, you win $2 dollars; if it shows tails, you win $5 dollars. If the coin lands on its edge, you lose $2 dollars; and if it disappears, you lose $6 dollars. What is your expected winnings when you flip this coin?

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