
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 modified coin has three potential outcomes per toss: it lands heads with probability $\frac{1}{4}$, tails with $\frac{1}{2}$, and on its edge with $\frac{1}{4}$. If it lands heads, you win $\$4$, if it lands tails, you lose $\$3$, and if it lands on the edge, you neither lose nor win anything. Calculate the expected value, in dollars, of playing this game once.

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