
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 special coin is designed such that the probability of flipping heads is $\frac{2}{5}$, and the probability of flipping tails is $\frac{3}{5}$. If you win $\$4$ for flipping heads, and lose $\$3$ for flipping tails, 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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