
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
On the game show $\text{\emph{Wheel of Fraction}}$, the spinner has been redesigned. Now, the spinner has six regions each represented with different monetary values or functions: "Bankrupt," "$\$1000," "$\$200," "$\$700," "$\$500," and "$\$400." What is the probability that a contestant will earn exactly $\$1600$ in their first three spins? Assume each region has the same area.

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