
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 fair 6-sided die is rolled. If I roll $n$, then I win $(n^3 - 2n)$ dollars if $n < 4$, and $n^3$ dollars if $n \geq 4$. What is the expected value of my winnings? Express your answer as a dollar value rounded to the nearest cent.

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