
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 $\text{\emph{Wheel of Fortune Expanded}}$, you see the following spinner. Given that each region is the same area, what is the probability that you will earn exactly $\$700$ in your first three spins? (Assuming the wheel is divided into equal parts and has four different money values, plus one "Bankrupt" region.) [asy]
import olympiad; import geometry; import graph; size(150); defaultpen(linewidth(0.8));
draw(unitcircle);
string[] labels = {"Bankrupt","$\$200$","$\$300$","$\$100$","$\$1000$"};
for(int i = 0; i < 5; ++i){
draw(origin--dir(72*i));
label(labels[i],0.6*dir(36 + 72*i));
}
[/asy]

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