
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 dice game uses a six-sided die with the following probabilities and outcomes: rolling a 1 or 2 gives \$2, rolling a 3 or 4 gives \$4, and rolling a 5 or 6 loses \$6. The probabilities of rolling a 1, 2, 3, 4, 5, or 6 are $\frac{1}{8}$, $\frac{1}{8}$, $\frac{1}{4}$, $\frac{1}{4}$, $\frac{1}{8}$, and $\frac{1}{8}$ respectively. What is the expected winnings from playing this game? Express your answer as a dollar value, rounded to the nearest cent.

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