
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 lands on 1, 2, or 3 with probability $\frac{1}{6}$ each, and on 4, 5, or 6 with probability $\frac{1}{2}$. Landing on numbers 1 through 3 gains $\$2$, but landing on 4, 5, or 6 loses $\$5$. Calculate the expected value of a single roll of this die.

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