
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 with numbers 1 to 6 gives a number 1 with a probability of $\frac{1}{4}$, and any other number with equal probability. If rolling a 1 wins you \$8, while rolling any other number costs you \$3, compute the expected value, in dollars, of your winnings after one roll.

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