
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 a probability of $\frac{1}{3}$ to land on a number from 1 to 3, and $\frac{1}{6}$ for numbers 4, 5, and 6. Rolling a number from 1 to 3 gains $\$4$, while rolling a 4 loses $\$2$, a 5 loses $\$5$, and a 6 loses $\$7$. What is the expected monetary outcome of a roll? Express your answer as a decimal rounded to the nearest hundredth.

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