
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 biased die has six faces, with the probabilities of rolling a 1, 2, 3, 4, 5, or 6 being $\frac{1}{6}$, $\frac{1}{6}$, $\frac{1}{6}$, $\frac{1}{6}$, $\frac{1}{6}$, and $\frac{1}{6}$ respectively. If you roll a 1 or 2, you win \$5; for a 3 or 4, you win nothing; and for a 5 or 6, you lose \$4. What is the expected value, in dollars, of your winnings after one roll?

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