
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 $\text{\emph{Wheel of Fortune Plus}}$, you see the following spinner. Given that each region is the same area, what is the probability that you will earn exactly $\$2000$ in your first three spins? [asy]
import olympiad; import geometry; import graph; size(150); defaultpen(linewidth(0.8));
draw(unitcircle);
string[] labels = {"Bankrupt", "$\$500$", "$\$700$", "$\$2000$", "$\$300$", "$\$800$"};
for(int i = 0; i < 6; ++i){
    draw(origin--dir(60*i));
    label(labels[i],0.6*dir(30 + 60*i));
}
[/asy]

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