
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 specific weighted die, when rolled, shows a 6 with probability $\frac{1}{4}$, any number from 1 to 5 (each with equal probability) with the remaining probability. If it shows 6, you lose 2 dollars. If it shows an odd number (1, 3, 5), you win 2 dollars. If it shows an even number (2, 4), you win 4 dollars. 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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