
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 coin flips heads with a probability of $\frac{2}{5}$ and tails with a probability of $\frac{3}{5}$. You play a game where if you flip heads, you win $\$4$, but if you flip tails, you lose $\$1$. What is the expected value, in dollars, of your winnings after two flips?

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