
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 uniquely designed die is shaped such that when tossed, the probability of a face labelled "Star" showing up is $\frac{2}{5}$, while the face labelled "Moon" comes up $\frac{3}{5}$. If you win $\$4$ upon the die landing on "Star" and lose $\$3$ when it lands on "Moon", what is the expected value, in dollars, of one roll of the die?

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