
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 three-sided coin has a $\frac{1}{4}$ chance of landing heads, a $\frac{2}{4}$ chance of landing tails, and a $\frac{1}{4}$ chance of landing on the edge. If the coin lands on heads, you win \$4; if it lands on tails, you lose \$3; and if it lands on the edge, you neither win nor lose anything. What is the expected value, in dollars, of your winnings after one flip? Express your answer as a common fraction.

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