
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
Each of $8$ balls is randomly and independently painted either black or white with equal probability. What is the probability that every ball is different in color from more than half of the other $7$ balls?
**A)** $\frac{17}{64}$  
**B)** $\frac{35}{128}$  
**C)** $\frac{1}{8}$  
**D)** $\frac{45}{256}$

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