
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 particular coin is biased so that the probability of getting a head is $\frac{1}{4}$ and a tail is $\frac{3}{4}$. If we win $\$4$ for flipping a head and lose $\$3$ for flipping a tail, what is the expected value, in dollars, of our winnings after one flip? Express your answer as a common fraction.

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